Neil A Mercer: I searched your older posts to refresh my memory. You started with the points and timing, and now you've gone through the fuel delivery system, including the carburetor. I would be pretty upset by this time, myself.
One Cheap thing to try: New Spark Plug.
Some forum members have reported unexpectedly good results from this simple action.
Another Cheap thing to try: New condenser.
If you haven't replaced it already, and even if you have, try another "known good" one. Even automotive capacitors will work, that's what is running on my Model 149.
If you've already tried these items, and you've been able to eliminate a mechanical source of failure (valves, cam, ACR), after a good night's sleep, I think I would try to monitor what is happening as it dies and backfires. That is, put a "spark tester" in line with the spark plug, and either use a mirror or have a second person operate the tractor so you can monitor the fuel into the carb.
For your situation, what I keep coming back to, is that the thing will start. Obviously, that means that enough of all the necessary components are there to "get the ball rolling" --compression, spark, and fuel-- so something must be happening AFTER the engine starts:
Hey, I've got it!
I'll bet your exhaust flow is blocked. It would explain all your symptoms.
The cure is easy: remove the muffler, with a hack saw if necessary.
Another possibility is a problem with the exhaust valve, but I don't see how the exhaust valve could work well enough to allow the motor to start, but then fail so quickly; the engine usually has to warm up a bit before the problem manifests itself, and if it is stuck open (it couldn't get stuck closed), its is easy to check its operation by listening closely as you turn the motor over, it will appear to have lost compression.
Anyway, its always darkest before the dawn; if you can stick it out a bit longer, I think you'll find the source of the problem, and it will feel so satisfying when you do.