Thinner tires up front are usually to combat understeer. The 350 and 370Z platform have a tendency to heavily understeer, someone correct me if I'm wrong in this. While I'm fairly familiar with the 350 platform, the 370 is still slightly new to me.
I feel like you probably expected this, buy why purchase a certain car when you can't afford to maintain it? Tires are a very basic thing that should be looked at cost-wise prior to diving into a purchase. I hope your situation is temporary and you'll be able to save for proper tires in the near future. Best wishes there.
Have you cost-checked 295/30s? $400-600 for two of these tires isn't bad.
Judging by your readiness to drop down to equal sizes all around, I assume you don't track it or drive aggressively. In this case, you won't need to worry about the best performing tires. What about some Ventus V12 EVO2s?
http://www.tirerack.com/tires/tires....omCompare1=yes
I would recommend replacing all tires at the same time, as different performing brands or treads aren't the best thing to have on a car.
Link for the fronts:
http://www.tirerack.com/tires/tires....omCompare1=yes