Yardman won't stay running?

Problem with Yardman Riding Mower with 13HP 4 stroke Tecumseh engine.
Lawnmower starts up easily, runs for a few seconds and then dies. When the choke is used, the mower will continue to run for several minutes but “stumbles” occasionally. Eventually, it will die.
Drained the gas and put in new gas. Didn't help.
Drained the carb and checked the float. Everything okay. Carb gets gas and float works.
Checked the gas line and filter. Everything okay.
Oil is okay and not gassy.
Removed the air filter (which was dirty). No improvement.
Cleaned the carb with carb cleaner. No improvement.
Checked the spark plug which was installed last fall after the problem first occurred. The mower had been run an hour or two with the new spark plug last year using the choke and dirty air filter. The plug was very sooty (not oily) indicating that the fuel mixture had been way too rich. Cleaned the plug, but no improvement.
So, the mower runs better with the choke on, but it is getting too much gas according to the sooty spark plug.
I jiggled all the wires and the mower ran much better for awhile, but then started doing the same thing: It would die without the choke being “On”. All the wires looked good and we couldn't repeat the improvement by jiggling the wires.
Any ideas?