I have a 76' 348 Cota. 2 things come to mind :
#1/ Even a new coil can be defective. And 30 years ago, I had the very same problem on a 2 stroke bike....and a 504 Peugeot car. Always easy start when cold, but very unlucky when warm. Sometimes I had to wait 5, 10 or 15 minutes. It ended up each time being a faulty coil. It is worth trying another coil ( and always good to have a spare anyways ! ).
#2/ As said by others here, the Mikuni carbs can act " weird ". On my Kawasaki KT250, the bike works just fine, but when off, fuel will seep past the bowl gasket, even with a new float valve and the proper float height. One thing you could try is to shut off the gas supply when the bike dies while ridding it. And try to restart it like that. If it does, it could mean fuel is going into the intake when the engine is off.
As far as the wires cut and exposed, some models came with lights. Maybe when the lights were removed, the owner back then just cut off the wires ? Anyhow, that should be cleaned up.
BTW, your bike seems very nice and I would like to see more close-up photos if possible when you get a chance !
Terry