Sounds to me as if there are particles of dirt clogging the idle circuit in your carburetor. May well also be a fault with the inlet needle and seat. These can wear, jam and soften in multiple different ways, causing all kinds of bizarre symptoms.
I notice you say you've "swapped in a carb". That suggests you bought a "remanufactured" carburetor from the parts store...yes? If so, you've set yourself back a lonnnnng way from achieving reliable running. Do you still have the original carb, or did you turn it in to get destroyed (oops, "remanufactured")?
For a possible quick fix, a couple of things you might try:
Buy a can of good-quality spray carburetor cleaner. My preference is for Berryman B12 in the red, white, and blue can. Put the little straw in the spray button.
1) Remove the air cleaner lid. Look down into the carburetor. You will see two black screwheads facing the sky, with a hole in the middle of each. Place the straw in each screwhead hole in turn, and give a good blast of carb cleaner. Do this with the engine off.
2) Carefully turn the idle mixture adjustment screw(s) clockwise, counting and keeping track of how many quarter-turns it takes to get each screw to seat lightly. Do NOT seat the screws firmly or you will damage the carburetor. Write down the number of quarter turns. Remove the idle mixture adjustment screw(s) from the carburetor. This may require defeating (breaking/prying off) the nylon caps on the screw heads, if so equipped. Have a helper start the engine and hold the accelerator so the engine is running at a very fast idle (it will not run at a normal slow idle with the screws removed). Give a few good bursts of carburetor cleaner in each idle mixture screw hole. Shut off the engine, lightly(!) seat the mixture screws, then turn them counterclockwise the number of quarter-turns you wrote down, plus one additional quarter turn, then back clockwise a quarter turn.
There's no guarantee this will fix the problem, but it might.
As far as your fuel filter being observably full when the engine won't start: I don't think that's causally related. If the carburetor float bowl is full but the engine stops running, as the engine coasts down to a stop it will operate the fuel pump a few times (as will you, when you crank the engine to try to start it). The float will have closed the inlet valve, so no fuel will be entering the carburetor, but the air bubble in the fuel filter can and will be compressed or displaced by liquid fuel from the pump. That's why I suggest the next step after flushing out the idle system might be to replace the inlet needle and seat and see if that fixes things up.
Any time I read about hot idle/hot start problems, I recommend the
fuel line mod. Please use a
metal fuel filter; the plastic ones are no longer safe.
Engine cleaning: Gunk Foamy Engine Brite if you're impatient, Simple Green if you've got time. Some of the paint WILL come off whether you clean the engine or not, and however which way you clean it.
Oil pan gaskets, regrettably, are 4-piece items.
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