[Arran]

I think that you could work it one of three ways, switch off the B+ voltage, switch off the filament voltage, or switch off the cathode connection. Switching the cathode connection won't work on many tubes because it is connected to the same pin as one end of the filament. I have an RCA that had a defective 6U5 socket where the B+ voltage lost it's connection to the target, the filament stayed connected, the result was a reasonably bright target but a weak testing triode. I would go with switching off the tube heater/filament, it's bad for a tube to be run for long periods without a plate voltage. In fact many Am/Fm receivers switched off the B+ to some tubes which resulted in them becoming stone cold dead for emissions.
Most of the eye tubes i run into are originals, the owners never replaced them, why? Because they are a gimmick, so it's no surprise that most are worn out.
If I had a set that used an American 6E5 I would probably get either a NOS or a good used tube, unlike the 6U5s they weren't used in as many radios. Contrary to popular belief you can run a 1629 on 6.3 volts without any ill effects if it has good emissions, it just takes longer to warm up, but you still need an adapter. However while the 1629 and Soviet 6E5s both have octal bases the pin-outs are completely different. You can still get Soviet 6E5s for a reasonable price but I can't see the advantage of using them unless you can get them in lots, by the time you make an adapter or replace the socket you will have more into it then just buying the proper American 6E5, even without the shipping cost.
Regards
Arran