... Anyway, I'm looking for some insight from anyone who may have seen or worked on this type of heater circuit. If you dare, take a look at the heater circuit in the preamp...
Overall, the amp has one heater system for the output tubes, and a second system for the preamp tubes. Output tubes are fed 6vac, but referenced to 25vdc (with a 25v electrolytic cap to chassis ground).
The preamp tubes have their individual heater sections arranged in series for 12.6v operation (instead of the normal parallel operation at 6.3v). Then, 2 preamp tubes are placed in series; nominally this would be 25.2v operation for the pair of tubes, but drawing 150mA total (instead of 600mA at 6.3v for standard heater wiring). There are 4 preamp tubes, and 2 pairs of tubes, each pair wired in this series manner and named "Fil A" and "Fil B".
For example, the input tube has the heater section of the 1st gain stage with pin 4 connected to circuit ground, and pin 5 for the 2nd gain stage's heater connected to "Fil A." This connection is shorthand for the heater section for the other gain stage receiving input from the 1st gain stage, at pin 4. This heater is then continuous with the heater section for the gain stage which follows, where pin 5 connects to 23v.
So instead of 25.2v, this preamp runs the heaters on 23v, which reduces emission and gain a little but also cuts noise a bit.
The source of 23v is shown down at the bottom left of the 1st page, and is a different, later node than the 25v reference for the output tube heaters. That reference is fed through R81 (4.7kΩ).
... Pins2 are fed by J13, Pins7 by J14.
J14 re-appears on Page 1, far right, second row of components connected to a relay. ...
Unfortunately, Peavey sucks. "J14" on the power tube page is almost certainly not the same "J14" on the preamp tube page.
Instead, to the left of the phase inverter shown in the bottom-middle of the preamp page, there are connections "To Power Amp Board" with the correct various signal and power connections, with the same physical spacing of 7-of-8 places of the ribbon cable & connectors. Unfortunately, they use entirely unrelated "J-" designators, so there wasn't an obvious way to match them up.
What is interesting is the
order of the connections differs between the preamp and power amp boards.

... I read no AC voltage there when the ribbon cable is connected to the power tube board. I do read +24VDC, though. ... When I disconnect the ribbon cable that sends the filament voltage to the power tubes, I do read 6VAC at the end that is connected to the transformer.
The reading of a.c. would seem to confirm the transformer and fuse are okay. The cap to ground could be bad; the presence of burn marks makes the ribbon cable suspect. I would at least try a different ribbon cable to rule that out (and 8 pin ribbon cable shouldn't be hard to acquire; unfortunately, if you're going to work on these kinds of amps, you'll need spare ribbon cables on hand).
What I don't get is why there isn't a resistor to ground for the d.c. reference voltage. Then again, the 4.7kΩ resistor may be intended to limit fault current to 23v/4.7kΩ = ~5mA, even in the event of the cap becoming a direct short to ground. That would make the burning improbable outside a tube failure. Maybe check the value of R81 between F3 and C55 on the power end of the preamp board. After that, you may be looking for secondary effects of board damage due to a past failure.