I'm havin the same problem with mine too. Took out yesterday and 1st time would not start. Took it all the way home , took off carb cover and sprayed out with carb cleaner and was able to get it running. So back to the lake we went and it ran fine for about 5 min. then it just died. Started again and had to half throttle back to the launch, it did run at that speed , shut it off then tried to start again , nothing. Got to be in the fuel system.
Ive been told you can not mix oils , but I have also been told you can add synthetic to the mineral but can't add mineral to synthetic.
From what ive read , better to be safe than sorry and completely empty out your oil resavoir and completely bleed the motor out too, and then run the synthetic.
You may have to pull carbs and clean internal filters as some how particles pass the inline filter and get gummed up in the carbs. I would also bleed the fuel system completely including tank and start out with fresh fuel, these are obviously process of elimination techniques but cheaper than a dealers mech charging you 90 bucks/hr to find the problem when this can be done by yourself with the proper shop manual and some mechanical knowhow.
Read the threads and there are guys here that can help you. good luck.