[snowman_al]

^^^ Understood.

A caveat before going any further with the separate HT transformer idea.
You have to make sure the transformer in the set is constructed as shown in the schematic and that disconnecting the chassis connection on the primary (mains) side does isolate the mains from the chassis. For example if the 2 secondary connections are internally connected to the primary for simplicity of construction.
You need to test this. Remove both primary connections from the transformer, then measure the resistance from the chassis to either of the transformer primary connectors. If you get open circuit (infinity) all is well. If you measure a/any resistance this scheme will not work. Let us know.

So a 'better' guesstimate of the HT requirement.
Look at the partial schematic in post #21 and R78 (270 ohms). That drops 20 volts so the current is 75mA and that feeds the majority of the set except for the ECL82 anodes. I have assumed they use 45mA each so they draw 180mA together. (That is from the ECL82 data sheet and the cathode voltages marked on the partial again.) Add them and you get 255mA, times the 240 volts gives you 61.2 watts. So again to be comfortable you need a 240 to 240 volt transformer in the 80 to 100VA range.

Note 1, if you go this route, you can easily change to full wave rectification (as David suggested in post #53) and that will actually reduce the 'stress' on the new transformer a little.

Note 2, even though I suggested the transformer idea, if this were my project, I would still go the Bluetooth or as you said opto-isolator way (yes plenty fast enough). They give you the protection you want via isolation and would be smaller and cheaper in the end.

Alan

PS I wonder what others think, please chime in.