[Mondial]

Eric, if the eye works on SW, then the 6K7 and eye tube circuit are working properly. The 6K7 screen voltage should rise as you tune in a station, which you confirmed when on SW. The whole system is dependent on developing enough AVC voltage to control the screen current of the 6K7. 

It appears that you are not generating enough AVC voltage on BC to control the 6K7. This could be due to a lack of gain somewhere in the BC antenna circuit, such as might be caused by an open coil winding, bandswitch contact, etc. Even though you are receiving signals on BC, there is not enough signal to activate the AVC, and thereby control the 6K7 and the eye tube.

Check the voltage on R1 to chassis ground, the 27 K resistor in the detector ( demod) circuit. There should be several volts of negative voltage there when receiving a strong signal on both BC and SW.