[Mondial]

Have you checked for out of tolerance resistors? The ones marked 15,16 and 48 are suspect, as they supply AVC voltage to the IF band RF tubes. 

It sounds like your AVC line is floating and reaching high negative voltages, cutting off the 24A IF amp tube. When you ground the 11 trimmer you are shorting the AVC voltage to ground. With the ground connected there is no negative voltage there and the IF tube works properly.

A bad tube can also cause this. Try changing the 24A IF tube and the 27 det/rectifier.

The RF coil resistance seems normal and would not cause the problem you are describing. If it measures 0.1 ohm it is definitely not open.

First AF plate voltage at 150V is normal when measured with a modern meter. The 45V reading was spec with the old 1000 ohms/volt meters used in the 1930's, which pulled down the actual voltage.

Cathode readings should be 2-3 V when measured to chassis ground. The Philco voltages were measured with their set tester, which measured to the filaments of the tubes not chassis. Filament winding is connected to the center tap of the HV winding and the BC resistor, so you have a 20 V difference due to the drop across the BC resistor #58.