Have you had a chance to thoroughly inspect the connections and ensure everything is snug and in the right place? Since you switched from a vacuum to a mechanical advance distributor, there might be something off there that's impacting the system. If the timing is too advanced, it could generate extra heat, potentially affecting the wiring. Double-check that the distributor is properly seated and secure.

Considering the history of your Type 181, take a look at the original grounding points and see how they're holding up.
Also, make sure the alternator output is within the specified range. An overcharging alternator can cause too much current flow, leading to the overheating issue.

 

if you can hook your battery up long enough check for shorts that can be pulling that much juice down. unless alternator turns out to be bad

 

You have a positive lead grounded somewhere. Probably in the ignition circuit because of when it happened.

Also of note, if the key is left on with the engine not running and the points happen to be closed, you coil is going to heat up and probably melt something. Its a VW thing...