I put this test circuit in LTSpice to simulate the architecture. Current Flows in the primary, the secondary cancels. If you lift the ground on the secondary center tap and place it on one end of the speaker load it works. No telling if the Tube will like the load, but feeding both ends of a center-tapped primary into the same tube seems to work. I would have thought it would not.
View attachment 988226
I think the individual legs of this OT are in anti-phase. Try it again with the upper inductors rotated 180 degrees.