There seems to be statements that could use some clarification. Are you saying that the oil checks low when it first shuts off and magically re-appears? I assume that you have a CV Kohler engine. Oil is checked by resting the top of the dipstick on the tube in its lowest position w/o turning it in. If yours has a low oil shut off, you could pull the wire and check your theory. Just don't let it ground or run out of oil. It is more likely that the hole in the fuel cap is plugged or that the fuel filter is improper on your tractor.

Many engines indicate a low oil level when first shut off.
The oil simply hasn't had time to run down into the sump from all the places it's clinging to.

I don't even think about trying to get an "accurate" reading unless the engine has sat for a few hours. It's a matter of learning "how low" you should expect it to appear upon initial shut off, to know if your level is "safe".

RE your engine shutting off-
When your engine dies, immediately check for spark. You may have a bad coil.

My STX38 has suddenly starting losing lots of oil. I will start with a full crankcase and can run the engine for about 20 minutes with no problems. After 20 minutes, blue smoke appears (not from the exhaust!) and it seems like it's running hot. I'll shut it down, wait several hours to check the oil, and the oil level will be quite low. The exhaust is not blue, and there is no puddle under the engine. So where is my oil suddenly going? The engine runs beautifully for the first 20 minutes until it acts like the oil instantly disappeared.

Check for a clogged crank-case breather. Might be the problem, since nothing else has solved the problem, RJ