[Putershark]

Such issues are sometimes better known as as "Hot Soak" conditions / issues and can be hard to find... These can range from

1. Fuel boiling (poor fuel or too low of an octane) in the lines. Next time (kill the smokes first) try taking off the fuel cap and see if that helps some Could be either poor fuel, fuel line pinch, loose fuel line connection OR a fuel pump that is starting to get weak. I would check the fuel filter condation at the same time also... Using garbage fuel to start your grill is one thing, it does not belong in your boat though and even more important if you go any distance offshore.
2. Various electrical connections (sensors) getting hot and expanding causing poor ECU function or creating ignition issues. I would check the condition (resistance readings) of the spark plug wires and replace either the wires or spark plug wire boots (depends upon how your wires are made), and then check to make sure all of your engine ground wires and both "clean" and secure.
3. Vacuum line getting hot and expanding with a hairline crack (though rare) throwing off the air fuel mixture. Some engines have vacuum lines all over the place and that is a lot of possible places to develop a leak.
4. Gasket expansion in or around the intake or intake manifold causing a air fuel mixture issue. You have to remember that anything leaking air "past" (afterwards) of the throttle body the engine ECU really cannot make adjustments to the air and fuel mixture to compensate for what is then known as "lean out" condation (to little fuel for that amount of air). And once you get either enough engine heat and or cooling again to seal everything back up, the programming in the ECU then matches how the engine was "designed" to run...
5. The dealership should have some testing equipment that they can use to pull (if present) some fault codes from the engine's ECU. The fault codes though do not tell the full story... It can read that the O2 sensor is working out of spec for example, when in fact the wire going to the O2 sensor (or some other loose ground wire) is the real problem. The fault code is just that, a fault code... And it still requires a human to interpret these readings and take the logical course of action to effect (and test for final Q/C) the needed repairs. This and NOT just start replacing a bunch of parts in the "hopes" of finding the culprit. This becomes even more important for you and your wallet as these engines go out of warranty and you are having to float the bill for all of this repair by experimation

Let us know how you make out and the final fix will ya!