It would seem to me that a series filament "cathode"  circuit  is different than a series heater circuit.

Series heaters as in the ARC-5 radios will make no difference in the circuit operation since the cathode is isolated from the heater.

In these old types, the series filament IS the cathode so current from one stage will flow into the other, providing a sort of negative feedback?

There are no bypass caps on the series connection to prevent this.

With the cathode types , the heater is now just resistor being introduced between the stages .

I would suppose that wiring the the cathode to the ground side makes sense and the "floating cathode" would be connected to the center connection.

Alternatively, maybe try a "no feed back" scenario by putting the cathode connection on the "hot side of the filament and using a large ceramic bypass cap to ground where the filament power enters at the first tube in the chain. ( especially in the RF section).

Just some random thoughts to consider...