Perhaps there is a bit of leakage of the float valve when not running, flooding the engine? Try loosening the tank cap when stopped to prevent any pressure buildup that may cause the mentioned flooding.
But I would highly suspect a coil secondary winding. Sure, a MercTronic tester would be great, but chances of a novice having one are nil. A multimeter ohms test is a good second best test.
Exhaust leaks, while a major problem, wouldn’t cause hard starting, since not running there is no exhaust.
Don’t be afraid to try choking it for one pull as a try. Some motors need to be choked even when warm.