99 Johnson Warm Start/not start

If anybody has any ideas about possible solutions, I would really appreciate any help available. I have had this thing in three times to 2 different places, nobody has been able to fix it.
I have a 1999 Johnson 200 Venom and it has always been a little touchy, but, not to this extent. It refuses to even start anymore after I have run it for more than ten minutes and then turn it off and try to start it again.
It will start cold great and run great for as long as I keep it running. If I turn it off and do not get it started on the first attempt, it will not start anymore and I have been stuck on the lake more than a couple of times. I am close to just giving up and selling it as I can not even enjoy myself on the water.
If anybody has any suggestions, I would really like to thank you in advance and appreciate any type of help possible. I like fishing and I use to love my boat, I do not want to get rid of it.

Visually inspect the stator under the flywheel closely (very closely). Take a good look at the two black coils that are located to the rear of the stator. If either of those black coils are cracked and/or leaking a substance down on the powerhead area, replace the stator.

The stator is a two fold component. The small series of coils pertain to the battery charging system. The two large black coils provide approximately 300 AC volts to the powerpack capacitor which is needed to energize the powerpack. When those black coils start to melt down, that results in a voltage drop to the powerpack which in turn results in weak, erratic, and eventually no ignition.

When this condition first starts (meltdown), the stator may provide ample voltage to energize the powerpack BUT as the stator heats up, the voltage drops which affects the ignition.

Let us know what you find.

Hey Joereeves,
thank you very much for responding so quickly and thank you for the advice. I took a look at the area that you told me and I am hoping that I am looking at the right wires. These two were at the back of the stator and toward that powerpack, but, not over the power pack. Both the sets of three wires that I think are the ones I am suppose to be looking at had two covers over them, but, one of the sets of wires looked to have some black goo coming out of the bottom of it.
Please take a look at the pictures below, they are tough to see because I was getting so close, but, let me know what you think. If I have to cut off those protective covers, let me know.
Again, thank you so much for your help. If I can get this figured out, I would be so relieved.

That's the general area BUT I'm not speaking about wires.... I'm speaking about the two large Black coils at the rear of that stator. The substance I speak of would be dripping from the black coils if they're melting down.

The pictures unfortunately are taken at a downward angle which prevents me from acually seeing those black coils. Use your own judgement.... if they're leaking, melting down, oozing a substance out of them, replace the stator.

Be sure to torque that flywheel nut to 145 foot pounds, otherwise the flywheel key will shear which will result in damage to the flywheel and crankshaft tapers.