[Arran]

You can usaully tell if the coil has been smoked by a lightning strike, the whole primary winding will look black. I recently ran into this in a lake 40s Viking battery radio (Dominion Electrohome) although it is broadcast band only so it doesn't have any extra taps. I'm not sure why they would connect a resistor between a dead coil and ground, the usual quick repair is to connect a capacitor from the antenna terminal to the secondary in some way. I've also seen this happen with an oscillator coil, a paper cap shorted out between the top of the winding and the B+, since most coil windings are made of very fine wire the internal resistance causes them to burn up. It was a rather stupid design in my opinion, much like the tone controls with B+ on the wiper capacitor.
Regards
Arran