We can draw a few conclusions from the original tube complement. 6.3V heater current is 1.5A or so, 5V heater current is 2A or so. No reason to doubt that, just because the good folks at Howard Sams tested a related unit and got a (very slightly) different answer.
The real question that remains open is, how much current can we rely on the high voltage winding to supply? Probably not terribly much - the single 6K6 is our clue there. 25 mA average, 28 mA peak current, 4 to 8 mA screen current, so let's call it 30 to 40mA required for the 6K6. The rest of the preamp tubes would have added perhaps 10mA current draw on top of that.
So Howard Sams is probably not too far off calling it a 50mA high voltage winding.
Should be ok for a Champ, or even a single 6V6 plus reverb or tremolo, but probably not ideal for a push-pull amp.
Here's a circuit that I've had a lot of fun with, it's a very slightly modified Supro 1616T (a/k/a Gretsch 6151.) Mine started life as a single 6V6 radio, very similar to yours, with a modest-sized power transformer. Buildable on terminal strips, for sure.
Mods were just a few tweaks to the tremolo circuit to slow it down a little and extend the range of speed, the only change to the audio circuit was the switchable cathode bypass cap. I settled on this circuit because I wanted something Champ-ish but with tremolo and this delivers the goods - the trem is quite good if I do say so myself. I used a Hammond 125CSE single ended output transformer, which has plenty of balls for a single 6V6 - maybe slightly overkill - I run it through a single 12" speaker and it's much beefier than you'd expect. You might have the 6K6's output transformer left over from your salvage operation though?
View attachment 763815 This is what the chassis looked like with the original output transformer still in place, and the big tuning capacitor for the radio removed:
View attachment 763819 Then I did a little origami on the sheet metal, and swapped output transformers.
Since it's a little head now, it gets to do all the thinking.
View attachment 763820 For convenience, I left the 2-prong convenience outlet in place, good for pedal power. That must've been there for an optional phonograph originally.
View attachment 763821 View attachment 763822