I am assuming you have a stock block.  The reason the hyper pistons are
not the best for a supercharged engine is that they can't take
detonation as well.  If there is no detonation then they aren't really
any worse than the stock forged ones.

IMO, there are other issues to worry about when pushing a stock block to
500+ hp. First is the main caps.  They aren't really up to the task for
high rpm horsepower.  Second, is the lifter valley of the stock 302
block is its real weak spot.  I can't tell you the number of blocks with
cracks down the lifter valley and there's not much you can do to
reinforce it.  Third, is the head bolts.  Go with 1/2" diameter bolts
instead of the stock ones.

I did run 16 psi of boost on my car but it was so sensitive to blowing
head gaskets from the heads lifting I went back to 12 psi.  If you don't
have detonation then the pistons and rods usually don't fail.  It is the
other things I mentioned.

I have also had my issues with the drive train.  The stock axles will
probably work well but the real problem will likely come from the
transmission (auto or manual) if it is stock.  I tore up a stock T-5 in
no time and went with a T-56.  The same goes for the clutch.  I  agree
that staying away from slicks will improve the odds of your drive train
components surviving.  I still have stock size axles and the 8.8"
differential on my car and they haven't given me any problems but I have
never run with slicks.  I don't think I would have any problems even if
I did as even then traction is somewhat limited.