Ok so I tried a bit of what was recommended, especially feeding the tubes that can, off of 12v directly.
I can get sound, and it's feeding the speakers sound that can get fairly loud. Only issue is, while it's seemingly not causing the volt meter on my car to go low at all, and voltages are ok and normal so far, but my check engine light oddly comes on, on super bassy music (like 90's alternative rock), and it's always the same trouble code from the cars computer, right O2 sensor read error.. Very weird, but when I disconnect the amp, the code goes away. It doesn't always do this with the amp attached though.
Anyway, here's an audio sample. I won't be able to keep this video up, it's being scrutinized for the music contents.
http://www.youtube.com/watch?v=_w-h263ur10
EDIT: And I did notice, at 1:28, when the songs bass starts playing, I have noticed some distortion in the bass guitar sounds. It's as if the tubes are possibly suffering from enough current, but are getting the voltage though.
For the other stuff that needs an inverter, I chose an inverter that produces the best sine wave, that I could find.