Voltage regulator problem with 1968 Dart

What key position when you measured this? When the key is in ACC position
So there was power available in the RUN circuit (ign 1) with the key in Accessory position.
There shouldn't be.
My suggestion is to disconnect the battery and do continuity checks rather than measuring voltage.

The fuse blows the second the kill switch gets turned on and providing power to car
Normally that would be a short in the wiring. Either the cigar lighter or the dome light feed wire is touching ground.
Disconnect the battery. Measure for continuity between the fuse terminal and the body ground.

MSD Ready to run distributor with no box, MSD Blaster2 coil wired per MSD directions
Doesn't help us much. Where does the RTR distributor connect?
Where it was connected may or may not relate to the VR letting out smoke.
But start here, whith what 67Dart273 has suggested a couple times. Its the right place to start looking.
I tell you again. Check the field to alternator case for resistance, check the green wire for shorts, and check the VR for being grounded.