Sounds like carburetor problems.
Start with the basics, a compression check.
If that is good, then it's sounds like carburetion.
Q-jets aren't your friend here. They belong on tow trucks and motorhomes. (In my honest opinion)
Tuning a q-jet can be done, but isn't as simple as a Holley.
Metering rods and and jets for a truck and usually too lean for a jet boat. The idle quality sounds like something is suspect. Q-jet should have a good idle, even on a jet boat.
Fuel pressure sounds like it's not steady at 7ish lbs to keep you running.
Non vented fuel tank(s) could cause this too, as well as a clogged fuel filter.
Several things you need to look into.
Make sure initial timing is good to go and your ignition system isn't failing either (bad coil or module?)
Dan'l
Just my $0.02.