Fred, you might try checking the spark immediately after shutdown when it is hot, in case the coil is on the way out.
The large one piece flo-jet is a good carburetor and its choke is manual, so unless for some reason you were choking it deliberately when it's hot, that shouldn't be the problem. Lowering the float level would make it leaner: do you have any reason to think it is rich? You can check this by inspecting the spark plug colour. There is a possiblity that you have a slow-flooding situation, due to a leaky needle and seat. Problems of this kind are fairly common with an elderly large flo-jet, and it matches your symptoms quite well if you are turning off the fuel when you leave the mower standing for a long time, but not when you leave it for a short time (that is, it is still warm when you restart). You can check this in various ways, but perhaps the quickest and easiest is to compare its restart with the fuel turned off while stopped, and with it left on while stopped. Do not leave the fuel on overnight even for a test, because if it floods the carburetor it will run into the cylinder and end up in the sump, so you'd have to change the oil before you could run it.
If you turn out to have a slow flooding problem, I can explain easily what you can do about it. Also, can you post pictures of the mower and the carburetor, and give us the model/type/code information stamped on the cooling air cowl please?
