Hmm...
This is not legal advice, but IMHO, you owe him an apology. He gave you two warnings before he kicked you out. Trust me on this; you *do not* want a reputation of suing clubs who stiff you.
Were you playing at your normal volume level or lower?
$0 is not acceptable because you provided what you agreed to provide (your standard musical services at your normal volume), and the fact that your band's normal volume was too loud for this particular club is arguably their problem, not yours. If they want quiet, they should have hired a jazz trio. Think of it this way: You don't hire Metallica and then get mad when they blow the roof off the place. You also shouldn't get mad if you hire a 6-piece electric band for a bar and they are too loud to talk over, assuming they are not playing extra-loud on purpose.
On the other hand, a professional, competent drummer (and your band as a whole) should be able to use dynamics to suit the room, within reason, given the limitations of the lineup and the genre. If you performed less than professionally (drummer included: he is part of your band and represents all of you; if your collective fault if your drummer is too loud, so don't single him out), you should not be entitled to the whole $350.
Consult one of your attorney buddies, and see if s/he thinks it's a good idea to write a letter offering a settlement of $175, considering it's both your fault that you were behaving unprofessionally (too loud), and the bar's choice to stop the show early. (A bar deciding to cancel or end a show early ordinarily means that you still get paid the full agreed-upon figure, unless your contract says otherwise.)
Personally, I would apologize in the letter for playing too loudly to suit the room, but still explain why I think $175 is fair instead of the full $350, considering that you provided your normal services as agreed, and they are the ones who made the choice to ask you to stop early, knowing that sans a contract stating otherwise, they're still responsible for paying you as agreed.
P.S. Next time, either use an electronic drum set (I own a six-piece Roland TD-6SXT, even though I don't play drums, for this reason), or get a different drummer. Also, have one of your lawyer buddies draft you a performance agreement, so you don't have this problem again. You should *never, never, never* gig without a contract. The fact that you have lawyer connections makes this even more inexcusable. Frankly, if you get any money from this at all, be grateful