The back pot will be the center shaft, which extends out further than the sleeve of the front pot, making it vulnerable. The thrust is probably on the back of the back pot for the center shaft. A blow (likely in shipping) may have pushed on the rear pot until the tabs that fasten it piggyback to the other section folded out and rendered the rear pot loose. Ditto the tone control. If the rear pot's wiper assembly pushes back far enough then the wiper will fail to make proper contact with the center (wiper) terminal or the carbon track, causing your signal loss trouble. You need to try to push things back into marriage, and bend the retaining tabs back where they belong.
As for the filament wiring bear in mind that the All American Five have filaments that add up to total the line voltage. Your set may require a bit more creative engineering, involving multiple series strings.
Dunno about the transformer thing.....
