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A claim for false imprisonment is unlikely to succeed.

False imprisonment is called a variety of things---like felonious/misdemeanor restraint, unlawful detainment, etc.---depending on where you live. To prove it (and generalizing a bit since this varies by state), you typically have to show (1) detention or restraint against your will, and (2) unlawfulness of the detention or restraint. A big challenge here is that courts often interpret this to mean detention or restraint by exercise of force or threat of force, as in Harris v. Stanioch, 150 Wash. 380 (1928) for example. The protesters are just in the way, so it's unlikely this would hold up.

Self defense almost surely won't be a viable excuse.

The idea of driving the car slowly through the crowd relies on the notion that you should be able to escape the alleged detention. The escape you're considering in driving through the crowd likely comes at the expense of making contact with members of the crowd. Making unprivileged contacts might be allowable in self defense. However, self defense probably hold up either. Setting aside notions of proportional defense, you have to be defending yourself against something: force or threats of it by the protesters. So if they don't use force, or threaten it, against you, then your defense is going to be really shaky.

tl;dr

Hitting the pedestrians is a separate crime, even if they shouldn't be there.

Background

On a highway, you might have a legal right of way and therefore a claim against the pedestrians for failing to yield.

Since the states (and not the federal government) own and operate the interstate highway system, your specific answer depends on the state law.

In North Carolina, for example, pedestrians walking along or upon a highway have a statutory duty to yield the right of way to all vehicles. So you could probably videotape and press misdemeanor charges against them individually. That said, contacting the police and waiting (or taking an alternate route) is the best recourse.

Having the right of way (or feeling ethically justified) doesn't allow you to commit an offense like hitting a pedestrian.

The fact that the pedestrians aren't supposed to be in your way is of little consolation in the charges you'll face if you injure or kill one. The court will see this as a legal/ethical problem, but one that won't go in your favor.

In particular, you deliberately directed your vehicle into the crowd with the knowledge that the action might cause harm. One doesn't have to imagine the Austin Powers steamroller scenario to know that injuries are possible when cars go through crowds. That will pull all of the "involuntary"-flavored mitigations off the table.

In particular, driving a car into a crowd might be considered "an inherently dangerous act or omission, done in such a reckless and wanton manner as to manifest a mind utterly without regard for human life and social duty." In the worst case scenario, where someone died as a result, you might be looking at second-degree murder in North Carolina. In that case, as a defendant, you'd hope your charge could be mitigated down to something like death by vehicle (which is similar to "vehicular manslaughter" in other states), and you'd shoot for the misdemeanor version of death by vehicle since you weren't driving under the influence. However, a key element of proving death by vehicle is that you unintentionally caused the death---and the fact that you deliberately drove into the crowd might ruin your defense. In the case where you just hurt someone, you'd likewise hope to mitigate intentional charges to unintentional ones.

tl;dr

Hitting the pedestrians is a separate crime, even if they shouldn't be there.

Background

On a highway, you might have a legal right of way and therefore a claim against the pedestrians for failing to yield.

Since the states (and not the federal government) own and operate the interstate highway system, your specific answer depends on the state law.

In North Carolina, for example, pedestrians walking along or upon a highway have a statutory duty to yield the right of way to all vehicles. So you could probably videotape and press misdemeanor charges against them individually. That said, contacting the police and waiting (or taking an alternate route) is the best recourse.

Having the right of way (or feeling ethically justified) doesn't allow you to commit an offense like hitting a pedestrian.

The fact that the pedestrians aren't supposed to be in your way is of little consolation in the charges you'll face if you injure or kill one. The court will see this as a legal/ethical problem, but one that won't go in your favor.

In particular, you deliberately directed your vehicle into the crowd with the knowledge that the action might cause harm. One doesn't have to imagine the Austin Powers steamroller scenario to know that injuries are possible when cars go through crowds. That will pull all of the "involuntary"-flavored mitigations off the table.

In particular, driving a car into a crowd might be considered "an inherently dangerous act or omission, done in such a reckless and wanton manner as to manifest a mind utterly without regard for human life and social duty." In the worst case scenario, where someone died as a result, a North Carolina prosecutor might push for second-degree murder (which operates on a "recklessness-plus" standard and might not be as crazy as it sounds since driving into the crowd is likely reckless, and driving in slowly with them yelling at you to stop could push a jury over the top). In that case, as a defendant, you'd hope your charge could be mitigated down to something like death by vehicle (which is similar to "vehicular manslaughter" in other states), and you'd shoot for the misdemeanor version of death by vehicle since you weren't driving under the influence. However, a key element of proving death by vehicle is that you unintentionally caused the death---and the fact that you deliberately drove into the crowd might ruin your defense. In the case where you just hurt someone, you'd likewise hope to mitigate intentional charges to unintentional ones.

tl;dr

Don't hit the pedestrians.

Background

On a highway, you might have a legal right of way and therefore a claim against the pedestrians for failing to yield.

Since the states (and not the federal government) own and operate the interstate highway system, your specific answer depends on the state law.

In North Carolina, for example, pedestrians walking along or upon a highway have a statutory duty to yield the right of way to all vehicles. So you could probably videotape and press misdemeanor charges against them individually. That said, contacting the police and waiting (or taking an alternate route) is the best recourse.

Having the right of way (or feeling ethically justified) doesn't allow you to commit an offense like hitting a pedestrian.

The fact that the pedestrians aren't supposed to be in your way is of little consolation in the charges you'll face if you injure or kill one. The court will see this as a legal/ethical problem, but one that won't go in your favor.

In particular, you deliberately directed your vehicle into the crowd with the knowledge that the action might cause harm. One doesn't have to imagine the Austin Powers steamroller scenario to know that injuries are possible when cars go through crowds. That will pull all of the "involuntary"-flavored mitigations off the table.

In particular, driving a car into a crowd might be considered "an inherently dangerous act or omission, done in such a reckless and wanton manner as to manifest a mind utterly without regard for human life and social duty." In the worst case scenario, where someone died as a result, you might be looking at second-degree murder in North Carolina. In that case, as a defendant, you'd hope your charge could be mitigated down to something like death by vehicle (which is similar to "vehicular manslaughter" in other states), and you'd shoot for the misdemeanor version of death by vehicle since you weren't driving under the influence. However, a key element of proving death by vehicle is that you unintentionally caused the death---and the fact that you deliberately drove into the crowd might ruin your defense. In the case where you just hurt someone, you'd likewise hope to mitigate intentional charges to unintentional ones.

tl;dr

Hitting the pedestrians is a separate crime, even if they shouldn't be there.

Background

On a highway, you might have a legal right of way and therefore a claim against the pedestrians for failing to yield.

Since the states (and not the federal government) own and operate the interstate highway system, your specific answer depends on the state law.

In North Carolina, for example, pedestrians walking along or upon a highway have a statutory duty to yield the right of way to all vehicles. So you could probably videotape and press misdemeanor charges against them individually. That said, contacting the police and waiting (or taking an alternate route) is the best recourse.

Having the right of way (or feeling ethically justified) doesn't allow you to commit an offense like hitting a pedestrian.

The fact that the pedestrians aren't supposed to be in your way is of little consolation in the charges you'll face if you injure or kill one. The court will see this as a legal/ethical problem, but one that won't go in your favor.

In particular, you deliberately directed your vehicle into the crowd with the knowledge that the action might cause harm. One doesn't have to imagine the Austin Powers steamroller scenario to know that injuries are possible when cars go through crowds. That will pull all of the "involuntary"-flavored mitigations off the table.

In particular, driving a car into a crowd might be considered "an inherently dangerous act or omission, done in such a reckless and wanton manner as to manifest a mind utterly without regard for human life and social duty." In the worst case scenario, where someone died as a result, you might be looking at second-degree murder in North Carolina. In that case, as a defendant, you'd hope your charge could be mitigated down to something like death by vehicle (which is similar to "vehicular manslaughter" in other states), and you'd shoot for the misdemeanor version of death by vehicle since you weren't driving under the influence. However, a key element of proving death by vehicle is that you unintentionally caused the death---and the fact that you deliberately drove into the crowd might ruin your defense. In the case where you just hurt someone, you'd likewise hope to mitigate intentional charges to unintentional ones.