[fenbach]

tom,
your resistance readings sure don't "add up." but you must be looking at the antenna transformer if it haws a center tap. it's part no. 1 on the schematic attached to your first post. the readings suggest maybe a short in the secondary coil?? even so, i'd wait before unwinding it. you can test the rest of the circuitry by putting a modulated signal into the grid of the 36 tube. i'd leave the antenna transformer out for now in case it is shorted. I still think the secondary of the RF coil, part no. 3, is open. it only has 4 leads, connected in pairs. again, you can check those resistances [2 low, the rest infinite] with the transformer in the radio. double check to be sure you really do have the RF transformer and not the antenna transformer. it's the one connected to the plate of the 36 tube. the antenna transformer is connected to the grid [cap] of the 36.
funny [to me] that changing the resistor would make a difference. you might check the capacitor, part no. 12. those little guys typically don't fail, but maybe it's open.
good luck. and let us know.
bob