So this seems to be a random issue? The only other thing I can think of would be your electric choke is not working correctly.

The boat would start normally cold, but once the engine was warm it would be very hard if not impossible to start, and wouldn't want to keep running at low RPM. While you're skiing it would run pretty well off the secondaries, just rich but still lots of power. This one is pretty easy to test, just turn the key on and leave it on for a while and check to see the choke opens and stays open. I'd leave it that way for a couple of hours and check it every 10 or 15 minutes.

Good luck