It seems your high speed circuit may be too fuel-rich, thus removing the air box flame arrestor allows more air and compensates for the extra fuel.
I'm wondering if perhaps those carbs were rebuilt and the high speed mixture adjustment needle screws were left not fully closed to zero turns.
If this is the case the fuel mixture at/near high throttle positions would no doubt be too rich and I know this b/c I experimented with this very adjustment on my 951 and found the screw needed to be fully closed just as the Seadoo shop manual spec. advises. As I recall, I opened these high speed mixture screws about 1/2 turn as a test and lost some RPM at full throttle operation.
The high speed mixture screw is on the bottom of each carb and from the factory had a plastic position limiter cap snapped onto on the screw head, which can be turned by using a flat blade screwdriver. Look to see if the black plastic limiting cap was removed by someone (I like to remove and throw these plastic caps away b/c they make it impossible to adjust or remove the mixture screw) but despite if it's stiil has the limiter cap the adjust screw may have been turned if someone rebuilt the carbs.
So I suggest based on this new info you should check to make sure the high speed mixture adjustment screw is completely clockwise closed, attempt removing the plastic cap (if equipped) before trying to turn this screw b/c the plastic cap often is cracked thus spins by itself and doesn't grip the screw head as intended, thus only the cap turns and not the screw. Remove and throw away these two problematic plastic caps.
The high speed mixture adjustment screw your looking for is circled red in the drawing, buried but accessible from the bottom of the carburetor and located near the mounting flange (circled in yellow).
The green circle is the low speed mixture screw, notice it is a "T"-handled screw thus much easier to adjust if you can reach it, but you aren't experiencing a low speed operation issue thus you shouldn't need to adjust this one.
Further clarification: Both of these mixture adjustment screws are perpendicular to the carburetor bore, low speed screw on top of the carburetor and high speed screw (the one you want) on the bottom of the carburetor.
Also, a couple of photos of the screw and problematic plastic cap I recommend you remove from the screw head and toss into the recycling bin.
You're gonna need a mirror to accomplish this adjustment, and probably a source of light
I think if you try running without your air box you may see about 50RPM more but you will risk seizing your engine from a too lean fuel mixture, so I wouldn't try this for that reason and for the reason you gave, it's unsafe to run without a flame arrestor.
