1998 Ski Nautique Starts/Stops, no constant run

I bought a 98' Ski Nautique this year that had not been used much in recent years. The seller had it de-winterized before putting it up for sale and said it ran great (of course). I got it and the second time I had it out it died on me after it had been run for a while and warmed up. Then I started it back up and it immediately died. Started it again, it did its initial up-rev and died again. Then on the 3rd or 4th time it started and kept running like normal.
I thought maybe it was bad fuel from sitting for quite some time and not being used much, so I topped it off with new fuel and added sea foam for the next trip out. It went without incident.
A couple weeks later we were headed out again and backed down the ramp to launch and the boat would start, do its rev-up and then immediately die. Repeat about 6 times.
It finally started and ran like normal so we headed across the lake to our spot (about a 5-10 minute drive). About 100 yards away from the beach it cuts out and dies. Then I re-start it, it starts, revs up and immediately dies. Repeat 6 or 8 times. Then it starts and runs like a champ until the end of the day, when the cycle repeats again.
The problem is sporadic and impossible to duplicate. So far I've replaced both fuel relays and the fuel filter but couldn't get out before the weather turned to see if that fixed it. Both fuel pumps seem to be running fine as you can hear them fine when you turn the key. I'm pretty confident it's not the kill switch.
Another notable trait is that it seems to rev higher and longer than it should upon initial start-up, and takes a while to come back down to normal running rpm. I'm not sure if that's related or not. I know the GT-40's, and most others, do rev a bit on start up, but it seems higher and longer than normal.
Other options I'm checking into further are the anti siphon valve and the idle air control
Update:
I went to get my boat ready for summer today after it was winterized. I replaced the emergency kill switch today just in case it was an issue too. Put new belts on and went to start it up and... it started and revved up for a second and turned itself back off. After repeating that several times it would not stay running. It starts, revs for a second and shuts itself off. I replaced the battery terminals and put a new connection on the wire coming off the positive terminal, as I’’d heard that was a common problem (called the stay run wire or something like that). Still no luck, it continues to start and then shut itself off. I checked the fuel pressure, it’s at 40 when it pressures up and goes to 45 when it fires and then goes back to 40.
Seems like maybe the computer is shutting it off. It doesn’t have a crank position sensor.
Any other suggestions?