My 1984 Honda Magna 700 has a mysterious ailment. Can you think of anything me and the mechanic have missed?

The engine has some worn parts that is causing the oil pressure to drop when it's warm. I don't know what kind of mechanic you are taking it to, but Honda has a switch that kills the engine when the oil pressure drops. Hard to believe he doesn't know that. You could try a higher viscosity oil, but it may only help for a while. It's either the oil pump. or maybe the bearings. That's pretty early for an oil failure on a Honda.