Okay... I'm hoping someone here with more experience with big 100W tube behemoths than I will have a decent idea of what's going on.

I have a Fender Evil Twin... The 1994-2002ish model (two input jacks, no tremolo). Lately it's started to sound underpowered and distorting at low volumes. The usual Fender sparkle/shimmer in the mids and highs dies out too. But this only happens some of the time. The rest of the time it acts like it's old self (TONS of headroom, really loud, really shimmery in the mids).

Ordinarily I'd predict this to be bad power, but I've tried it a few different places AND through battery backup units used for computers (rated for 550W, so it should be able to draw as much as it wants) and the behavior remains the same. I've pulled all the tubes (which were replaced only a year ago and it's only seen occasional light use since) inspected them, and shot connection cleaner in just about everything. I dropped the chassis and shot connection cleaner and checked all the connections internally as well (any tech knows 90% of problems with 'working but misbehaving' amps are from loose or dirty connections).

What it seems like to me is that the amps internal power supply management (all the caps and such) isn't working as it should and that it's starving either the preamp or power amp tubes of power, thus dropping their headroom and causing early clipping?

I plan on taking it to an experienced tech (I don't want to mess with anything requiring me to drain 500V capacitors, thank you), but because it's a periodic problem that will only occur for certain if you play through it for several hours I want to have some idea of what's causing the issue before I take it in so I can at least give them something specific to look into.

If you have any ideas/experience with this kind of problem could you let me know the cause?

Thanks in advance.
I had a similar problem with mine except it was crackling a bit as well, I took it to a tech and it was just a few dry joints hopefully yours is a similar easy fix.
I tried pulling all my tubes and got nowhere, getting an expert is probably the best thing to do.