Had a similar situation in a home I lived in. We lived on the street closest to a High School's footbal stadium and the inadequate parking would cause fans to park in a manner that took a street that could handle bi-direction traffic to an unsigned one-way road. The school did make frequent announcements that fans parked there could be towed (it helped that I was one of many alums that lived there). The police informed me that unless there was some signage, they actually couldn't do anything. So you have the benefit of signage that says people cannot park there.
I would recommend calling the fire marshal. In Washington State (I assume your not in DC) the Fire Marshal is a division of the Washington State Patrol, the state police organization. Giving them a call in the evening when the parking is observably bad, will likely get the ball rolling. I would not expect towing, but I would expect to see tickets under offending vehicles if they come out.
If they fail too, I would start taking pictures of offending vehicles and present it to the local branch of WSP. I would minimize the inconvenience to your commute and the safety hazard of blocking space allocated for use by Emergency Service Vehicles. Try to get a name of someone who you can personally work with to assist you in the manner and who you can contact to report further issues. If they won't provide, ask if there is a way you can submit complaints to them.
I would, after contacting the WSP, notify your building's staff in person and through e-mail, that you have made them aware of the situation and that they have taken no action on previous attempts and that you have gone to the WSP over this matter. This serves two purposes, first you are notifying the building managment of a potential violation of law (the fire code is a law and is there because it's easier to fight deadly fires by removing hazards that make fires deadly in the first place. If a fire truck is blocked from the fire lanes, the fire fighters are going to have to deal with that before they can get to doing their real job.). The other benefit is to create a paper trail, which you can present to the WSP to show the building is compliant in fire code violations despite being made aware of the problem. Your building is likely not doing anything because there's no documentation that they are aware of the problem, so they can claim they didn't know anything about this if it goes to court.
Finally, I would recommend you seek an attorney that specializes in teneat or real estate matters and ask for a consultation. You do not have to employ their services, but most law offices will have a "client intake" process where you can explain your case and they can offer you some advice or other avenues. Even if you don't intend to sue your landlord(s), and even if you are reporting a crime to police, having a lawyer when dealing with the police and landlords can only help as they will be able to better advise you so you can do this safely without exposing yourself to civil or criminal liability. You can bet they have lawyers that will be more than willing to screw you for their clients. Also, even if you have no intention to go to court over this, they do not need to know that.