Oil fouling is usually a gradual, one plug at a time thing, not something that suddenly shuts one down.
But do look at the plugs, an oil fouled plug will be drippy wet with black oil to the point the gap is bridged with carbon. If it has a history of burning oil, go with a hotter plug. If the tractor only sees light duty, you can get by with a couple steps hotter plug.
It does sound like the advance is stuck, possibly the springs are broken or missing. You can drive out the roll pin that holds the gear on, pull the shaft, remove the point cam, clean and lube everything. Pay close attention to how everything comes apart. You may have to soak the point cam to get it loose if rusted badly. The advance gets light oil, the bushing gets high temp grease.
But before taking the distributor apart, look at the side play in the shaft. It needs to have very little side play. If the bushing is worn, the points will not stay set. You may be looking at buying a rebuilt distributor if the shaft and bushing are worn.
Or, install an electronic conversion kit. They are very dependable, don't mind a little shaft wear, and are a way around today's poor quality ignition points and condensers.
When timing the engine, there is a timing mark stamped into the flywheel. It is visible through a round hole below the starter, usually covered with a snap in plug. You will need to get #1 cylinder near TDC to find the marks. They can be very difficult to see, best to clean them off, mark with a white paint pen.
Once the distributor is back in, double check the firing order, check the spark at the plug end of the plug wires. Should get a 1/4" blue hot spark. If any doubt about the plug wires, replace them with spiral core or solid wire wires.
The intake backfiring can have several causes. Retarded ignition timing, and lean fuel mix are the most common causes. Crossed plug wires, bad plug wires, or moisture under the cap can also cause backfire. An exhaust valve not opening will cause rhythmic backfire under load. Look for a bent push rod, or flat cam.