John
I'm not an expert (there are plenty of people on this site who remind me of my status when I post), but based on my experience, I suspect your valves are sticking.
Tell me, how does it turn over when it stops?
If it turns over fast like it has no compression, it could be a sticking valve, probably the exhaust valve.
Working toward a resolution, since the problem is heat related, first make sure that the motor is getting all the air it needs to run cool. Best practice is to remove the shrouds and blow everything out.
If you suspect the valve, or just as good practice, replace the air cleaner so that you can be sure the mixture isn't leaning out, causing the motor to run hot. I replaced my air cleaner this year, and it made an immediate difference in how the engine ran, and in how much (less) smoke it produced on start-up.
I'm also a big fan of the low ash oil available at your local Cub Cadet or IH/Case dealer, the stuff really seems to help with the lubrication of air-cooled engines. It is also available from our sponsors.
Another "trick" is the use of Marvel Mystery Oil, in both the oil and gas. Charlie just posted his formula --one capful in the gas tank, and two in the crankcase.
I think a little loving care and maintenance will bring your 1430 back to life.