Is there any way to present a case to the grand jury if the prosecuting attorney is unwilling to do so?
To answer the first question, the answer seems to be "generally not." In federal courts, this is explicitly not allowed -- rule 6(d) of the Federal Rules of Criminal Procedure states that the only people who can be present before a grand jury are government lawyers, the witness being questioned, interpreters, and a court reporter
In state courts, the rules vary by state. However, again, private citizens are generally either completely not allowed to act as prosecutors, or are only allowed to act as prosecutors in a restricted set of situations and subject to the ultimate control of public prosecutors. For instance, in Virginia (which allows private prosecutors), the private prosecutor can't speak in front of a grand jury, initiate a criminal case, or participate in a decision to dismiss charges (page 23). In New Hampshire, private prosecution is limited to misdemeanors with no possibility of jail time, and again the state can dismiss charges (page 8). Rhode Island, like New Hampshire, allows private prosecution for misdemeanors but lets the state dismiss charges (page 11). The justification for allowing the state to dismiss charges is generally "prosecution is inherently a governmental task, so the government must retain ultimate control."
I would point to a concept that I feel to some degree answers your questions, the "runaway jury". The idea being that the jury finds itself unsatisfied with whatever it is the prosecutor is telling them, and moves on by itself.
Because of the investigative powers of a grand jury, the jurors could in theory investigate a matter on their own, even without the cooperation of the prosecutor.
Thus for example we have the case of a New York grand jury in the 1930s, who came to the conclusion that the prosecutor was corrupt, and went to the newspapers while continuing the investigation on their own, until a new prosecutor was appointed.