I would check the high beam switch, first. I had that exact same problem on my 67, and it was the high/ low switch.
Alternatively, if the "cheapest I could find" lights are getting abnormally hot, I would try other lights before diving too far into wiring and switches.
Alternatively, if the "cheapest I could find" lights are getting abnormally hot, I would try other lights before diving too far into wiring and switches.