555 and output amplifer with different Vcc supplies
I see two problems here:



1:
Tweeters can be rated for total system power, not their own individual power.
Pay very close attention to that when you read the specs.  Given a full-range audio signal, most of the power (80-90%, more for bass-heavy stuff) goes to the woofer(s) and the tweeter only has to handle what's left.  So a 200W system-rated tweeter may only be good for 10-30W on its own.



2:
Per your actual question, that circuit won't gain anything from the higher supply because it's set up as an emitter-follower.  For that design, the only benefit of a wider supply range is to prevent it from clipping because of the supply.  It will never exceed the voltage that it's driven with.

That being said, you can easily level-shift a square wave using an NPN to ground and a pull-up resistor to the higher supply voltage.  The low-level signal generator only sees the NPN and doesn't know about the higher supply, and the pull-up resistor only has to be strong enough to drive the base of the power transistor.  Given enough current gain in the power stage (I see you have darlingtons, which are known for exactly that), this shouldn't be hard either.

This will also invert your signal.  Inversions often come for free and sometimes have to be explicitly reversed.  If you don't care about that, then you're done, else you can add a second transistor + resistor to invert it back.  Only the last stage needs to share the higher supply.