Pork Pie or Gretsch Renown are usually $300 new, so either with a discount or buying used you can get one in your budget.
Another one to check out if you want new is the Pearl Session Studio Select, which is in your price range.
I know you're disappointed, but your preparation was definitely not for nothing! Whether your first gig is next week, next month or even later, you have that foundation to build on. Look at the bright side, if the gig is delayed it gives your group even more time to tighten things up.
You say you've learned the parts, that's the biggest thing! It's natural to take cues from the singer, but if she's unreliable that makes it even more important for you to lock in with the bass and guitar players to set and keep the tempo. I bet she's even more nervous than you since she's up...