Well, on the Gray lines, it sounds like you have done a bit of searching, and found what you need to know.
Here is a general overview:
The following items should be cleaned.
Filter on bottom of fuel baffle.
Fuel select valve.
Water trap filter.
Carbs, and carb filters.
Check vent hose, to be sure it is un obstructed. Those gray fuel lines crudded up EVERYTHING on mine, so I replaced all of them. Vent lines, pulse line to fuel pump etc. Some folks don't replace the vent line, but I did, and really can not see a good reason to leave such a Trojan as disintegrating fuel lines ANYWHERE that it could get into the system again.
This has been an interesting thread. Amazing what some folks will doo, to GO FASTER! (they think).
And, a minor comment on the starter. If somebody has been cranking it with that HIGH compression, the starter may be partially burnt out, due to heat. It was not designed to crank it with that much compression.
But, I'd thoroughly clean all the bat cables, (both ends) and re assemble with a pat of grease, to keep out corrosion, first, and if it did not work right, there is a possibility of a starter problem. Also, it is OK to JUMP one of these, so long as it is done in a well ventilated area, AND the HOST motor is NOT running. You can mess up the mpem if it is running. A weak battery is a common problem. You can confirm that it is not the bat, with a jump, and good cables. BTW, don't waste you money on cheap jumper cables! Get good Mechanics grade cables. Four aught (0000) copper is good! But, I digress!
Nothing like a Sea Doo, for a ride around the lake.
Hope you find and fix everything!
Nate