I touch the black and white wire going to the negative on the 2&3 coil and get a buzz with the key off. Is this significant? But no buzz on the 1&3 coil?
Mick - the BLK/WHT wire is switched power, not ground! This wire comes from your RH KILL/RUN switch. The "ground" for your coils comes from the points (BL and YLLW wires).
Your idiot lights are missing their BLACK wire connection which is why you don't have illumination.
Forget the Alternator; its not your problem. Its the BLACK wire within your harness somewhere. And here's why-
Your problem only occurs when you rotate the key (fuses blow) so that is a sure sign its along the
switched power side of things. If the BLACK wire rings out to ground anywhere along its branches, then you bike is sending 12v to earth, and that will cause a fuse to blow. Its as simple as that. You don't even need to run the motor to make the fuse blow when BLACK is shorted (this eliminates the REG, REC and Alternator).
Remove the tank. Pull the 2 fuses for TAIL and HEADLIGHT from the fuse block. This leaves you with MAIN. Flip the key. Fuse blow? If not, with your meter, check for 12v on the BLK/WHT wire at the coils. If 1 coil has it, but the other is shorting to ground, you will blow a fuse. This also explains why with the RH control disconnected you don't get a ground bell from the meter. You can verify this with the RH connected and the KILL/RUN switched to KILL (should be no ground tone) in RUN you should get your tone (only because you're wiring is wrong somewhere).
I'm not saying this is
the problem but if you indeed have BLK/WHT grounded at the cols, that is a
big problem.