Well to the left of coil in your first picture you see those diode boards. Gottlieb didn't put the diodes right on the coils. So if you removed it you should or will still have a diode on the board. Yes when coils overheat and the shellac coating melts or breaks down windings are shorted and the shorter the length of wire gets the less resistance you will get. Any 1n4001-1n4007 is fine as a replacement. Diodes are used as a voltage spike flywheel for back emf when a coil deenergizes. Banded side with any coil will always connect to the more positive side and unbanded will go ground. If a diode is replaced incorrect you will immediately blow a fuse and may cause damage as it will act as a dead short.