[Arran]

Try Edcore,, if you need a close electrical replacement, or see if you can find a used one that close, or find a NOS generic replacement like a Stancor, a Thordarson, etc. Brand Z transformers were notorious for being marginal at best so just about anything would be an improvement. Oh look, the dummies used a 6X5 to power a 6F6 output tube, and they are running it with 368 VAC on the plates and an output voltage of 325 VDC, not smart. The 6X5 has a max voltage rating of 325 VAC on the plates and current output 70 ma, did these geniuses leave their tube manual in the drawer when they designed this thing? The Philco sets that use 6X5s run them at much lower plate voltages, they used 41s or 6K6s, not 6F6s, and they used bigger power transformers. But the order of the big black dial will just keep repeating to themselves that the evil 6X5s are to blame, not idiots at brand Z ignoring tube specs.
I'm not big on altering a radio but the power supply in this set is so badly designed that you should do one of two things: Use a power transformer that has a lower voltage high voltage winding, and keep the 6X5, maybe keep the 6F6, but consider using a 6V6 in it's place, or a 6K6 but that involves using a new output transformer due to the plate impedance. Get a larger power transformer, with a 5 volt filament winding, with the same 350/368-0-350/368 volts on the high voltage side, dump the 6X5 replacing it with a 5Y4/5Y3, and keep the 6F6. Make sure that the speaker filed coil is alright, that may be toast too.
Regards
Arran