Thank you for the additional information.
The round clear plastic pieces are the check valves I was referring to. They are in fact directional, BUT, I have serious doubts that it would affect the way the ski performs. There is a blue line on each check valve that is supposed to be installed away from the aluminum block. I have looked for a difference of one side vs. the other side and cannot for the life of me find a difference, other than the blue line. I don't think going back into the carbs is indicated at this point. I am still impressed you could get it done and are even remotely volunteering to do it again.
In thinking deeper about this and based on the information that you never heard this engine run correctly, I have to ask if you checked the reed valves closely when you had the carbs off? If the engine were to get water in it below the piston when it comes down it forces it back out the intake and can break the reed valves. Just another thing to think about.
The idea I had about the fuel lines in the tank was if there is a crack or hole in them that would allow them to get air in the lines. It sounds like you replaced all the lines from the top of the tank to the carbs.
If you are re-using the electrics that came with the engine, perhaps we need to check them out to make sure we aren't dropping a cylinder as we try to rev it up. To do this, you will need cooling water. Either run it on the flush kit, leave it tied to the trailer and back it in the water so the jet is under water, or tie it to a dock, unless you are on a very un=busy body of water where you can ride it around a look at a timing light while underway. You will need an automotive type inductive timing light to check the ignition. Primarily we want to see if we are loosing spark to a cylinder as it revs up. Secondarily we would like to see the timing advance as it revs. You are going to need to be able to see the coupler to determine that. Which constitutes removing the plastic shield over the coupler, putting the front cylinder at top dead center, and making a mark with a magic marker on the top of the coupler, at 12:00. Start the ski and observe where the mark that you made is, then rev it and see if it moves (advancing) from there as you rev the engine.
One other thing to think about would be if the power valves are stuck down. At 5000 RPMs you should be able to see the pulley with the cables on it move along with the shaft that connects all the cylinders together. It is not unheard of for them to get stuck from being carboned up, and quite possibly from sitting too.
One last question I have would be did you take a look at the throttle plates and did they appear to be at the exact same opening at rest. This is carb sync and can negatively affect an engine's ability to rev.
Give those things a try and see where we are at.