I don't think it will like AC in the heater/cathode circuit, so you would have to sneak it in that way to isolate the heater from the cathode. Then just jumper the original filament terminals on the adapter.
All cathodes are grounded that way.
I'm pretty sure you will need DC if you attach the cathode to a filament lead. otherwise the AC will be injected into the signal path.
Dave got his working with just the conversion sockets and the original series wiring AFAK.
I'm thinking that perhaps bypassing the floating cathode pin to ground with a ceramic cap of say, 0.1 or 0.05 uf may improve the RF performance.
Adding another 100 uf bypass cap to the modulator cathodes may boost the modulation. ( DC mode only)
.
No wiring changes, just tacking on extra caps which is easily reversible.
Don't know for sure, just thinking out loud.