OK, here's what I can see from your measurements...
The 6.3V filament supply sits on terminals 22 and 24. Those terminals are both connected to pin 25 by 130 ohm resistors. 6.3V divided by the 260 ohms (the two resistors in series) is 24mA, which would be the expected current with a 300B sitting in the socket but no current being drawn from the HV supply.
Between 22 and 25, we see 3.4V, 3.4V/130R=24mA.
Between 24 and 25, we see 2.7V, 2.7V/130R=21mA.
These measurements tell me that nearly no current is being drawn across these resistors beyond just having the 6.3V filament supply active.
1.3V at terminal 25 indicates 4mA of cathode current, but this is a contradiction to what's going on with the HV side.
Just for curiosity's sake, if you run no 300B in the A socket with just a 300B in the B socket, what are the voltages at terminals 1 and 6?