OK, you had the bowls off, but did you remove and clean the high speed jets that are in the bowls behind the hex drain plugs?
Find something that can pinch off the hoses to the carb primer nipples. If you can’t find something to clamp off the hoses, simply remove and plug them two at a time…
Now try the primer again at high speeds where the engine falters. Repeat this until you have tried each cylinder on its own. Hitting the primer with all three hoses connected might have confused the issue a bit.
RPM should drop if the cylinder is firing correctly
RPM will pick up if there is a fuel supply/carb problem with the cylinder
RPM will stay the same if the cylinder isn’t firing, which doesn’t seem to be your issue
One final point. Sometimes those brass primer nipples of the carbs get plugged up with will confuse the issue because there will be no RPM drop/increase on a cylinder with a plugged nipple…
So, try pushing the primer at slower speeds when the engine is running OK (one cylinder at a time), the RPM should drop down because you are flooding the cylinder. Clean out the brass nipple if RPM doesn’t drop at lower RPMs.
I know we have discussed this before, but perhaps there is a fuel supply issue to the carbs…I think you have already had the filter cap off. Have you tried a separate 6 gallon tank and hose (make sure it is premixed 50:1). Have an assistant pump the primer bulb while the engine is misbehaving also…

Well, it does seem like some sort of fuel starvation issue from what you describe. But, that is just a guess, I am not there. Try the primer test and we will go from there. Does your inline filter show any signs of more debris? Just because the clear filter shows fuel flowing, doesn’t mean it is flowing properly, to all three carbs. Those little black plastic fuel line tees that distribute fuel to the three carbs could be an issue, those little fuel lines might be kinked or coming apart internally. I even had one relatively new engine years ago that had a piece of the steel float arm hiding under the float inlet needle seat cutting off fuel to one carb intermittently.
I’m hoping this is just an issue of that lower high speed jet having some debris in it, perhaps the broken brass ear is floating around in there.
Usually fuel pump issues occur at lower speeds, the engine won’t even get to high speed. There could be an air leak somewhere also. Or, the boat’s fuel system might be messed up creating a restriction/air leak. I am trying to remember, did you try a separate 6 gallon tank/hose?

This spring, I helped my neighbor with his 40, which has pretty much the same style carb design. As many times as I had done them before, somehow I put one float in upside down. The engines will run low speed okay that way but loose fuel at higher speeds on that carb if you make this mistake, which is easier to do than you might think….

frankr wrote:

Has anybody suggested water getting into a cylinder?

Not yet Frank, water intrusion is always a good possibility on these three cylinders with the complicated exhaust manifold…