Back your ski tied to the trailor into the water to put load on the impellor when you start motor. Then you can use your tach to set idle speed and low speed adjuster. If you still have problem starting in water, either the pop-off is wrong or too much clearance in the rotary valve cavity, and the RV cover would need to be machined to bring the squish back to spec. Usually this is the case with hot motors.
Normally not starting when in load of water is not enough fuel in the mix, too much air.
If won't run, test the Rectifier, use your voltmeter and test at 5500 rpm's. if it is 15vdc or more, the Rectifier/regulator is bad. Metal shaveings, bits, particles in a Stator are a death knock
on a Rectifier's door!
Open grey box and Disconnect the red wire to the rectifier and see if it run great. restart the ski several times to confirm and if everything worked, Rec is bad, This is the Rectifier test. Rectifier go "slpiftzt" when you jump start a ski with a dead battery most of the time. This is a Simple mistake anyone can make.
Also usually if compression is bad, is cause of not starting in water, because all the fuel in the cylinder is NOT being ignited.
What usually is killing a battery in a Sea Doo with trim is water in the VTS unit. Pull the cover off and see if that's the case. If so, disconnect the harnesses coming out of the VTS module and see if your drain goes away.
The module can corrode the reed relays and make the vts not only inoperable, but can stick and continuosly be a drain on the chargeing & electrical system. So that said, disconnect the VTS harness, and see if the problem goes away!