[codefox1]

Other than the pinout, the 5X4G and 5U4G seem to be pretty similar, and either one should work out, same PIV and filament requirements, according to my tube manuals. Both are octal based tubes. If the socket was replaced in the past. probably it developed arcing or physical damage. One point of caution when re-wiring, make sure that the "unused" terminals of the socket are not used for other components not related to the tube itself.

I do know that it is pretty easy to get a 5U4G, (and in fact any 5U4 later versions,) but it might be a little harder to scare up a 5X4.

I would defer on the field coil discussion to others. A resistor of the same value (and 25 watts at least) would preserve the balance of the B+. This is a seriously nice set, wish I had one, so please wait for more discussion before proceeding.