So I had all this typed hours ago and we lost power due to some storms. I digress......
Your boat is a 97 not a 98...I
suspect. 98/99 had different carbs and a totally integrated MPEM, not the remote grey box like yours has on the starboard side. 98 had the coil boxes over the rear driveshafts, 99 had them to the sides of the engines, yours are in the gray box. I knew something was up........What are the last 2 numbers of your HIN?
Ok, here's my list of what I don't like.
Air boxes---They HAVE to be on there, your carbs will never run right with out them. They're jetted to run with them. You should be able to set the carbs to spec on the bench, put them on and go, with the air boxes. I have NEVER needed to "tweak" carbs on a stock ski or boat. Only the idle and even that is rare. The dome goes up on the flame arrestors too, you have them upside down.
Blue spark plug wires. If they're automotive spiral wound, that could be an issue. These things are as basic as it gets. All they need it regular solid core plug wires, literally multiple strands of solid wires and good ole' NGK BR8ES plugs, not 7's, not 9's, not irriduim. If those wires have any "leakage" it could screw with the electronics. I think the manual calls out the resistance of just the spark plug boot alone--removed from the wire---check that. Then check the resistance for that blue spark plug wire, again, I think it's in the manual or that might be the coil test, still check the coil
Here's 9'-10" of the correct spark plug wire
SEA-DOO GTI 278001268 SPARK PLUG WIRE NOS 9' 10" OEM WATERCRAFT FREE SHIPPING | eBay
So, lets check a few things first.
Do you have fuel shut off valves?
Are your fuel pumps on the carbs or are they separate form the carbs like I posted pics of?
If I can see them correctly they're on the MAG carb in one of your pics---again leading me to believe your boat is a 97. If that is the case all your fuel lines supply and return etc... are all 1/4" no 5/16 fuel line at all.
Back to what I see:
Fuel return line---my god it's HUGE looking but it could be stock, the fuel supply line looks the same. It could just be the "burn jacket" to make it "safe". The fuel supply "probably" was 5/16" (inside diameter) originally from the baffle to the fuel filter , from the filter to the pump and from the pump to the carb. The rest is all 1/4", even the return. Throw all that clear/yellow fuel line out and get straight black ethanol safe fuel line. I know, I know, how do I know if there are air bubbles in my fuel lines??? Don't know, all the manufactures used gray or black fuel line---If they don't care neither do I. Just stay basic. Guys always try and one up the manufacturers. Use hose clamps on all the connections, you can get full stainless mini clamps at Home Depot. NO CABLE TIES. But like I said, if your boat is a 97 it should be all 1/4" as per the microfiche.
This should be your fuel system, yes?