If anything, removing the air cleaner (restriction) would make the air-to-fuel ratio greater (more air per fuel) and make your intake charge more lean than before. If the issue was just "too much" accel pump squirt/too "Rich" on takeoff, you could simply bend the linkage/adjust geometry to provide much less fuel, effectively build in a more "lean" mixture, and that issue would be moot.
But there are many cases in which these carburetors have failed the exact same way, and it's something that these adjustments won't be able to correct. Like Mike mayben said:
"the most likely issue is that the power valve actuator in your carb is non-func..."
if I understand this carburetor correctly:
your power valve is only supposed to operate (open) when vacuum drops enough that the engine needs more fuel to go with the sudden change in airflow caused by you opening the throttle plates. The actuator for the valve is just a metal rod contained in a tight-fitting bore that happens to be routed to a vacuum source. If this bore leaks, or if the passage is clogged up and will not allow the vacuum signal to travel, or if perhaps it is frozen in place, or if... [etc], the power circuit does you no good and makes these carburetors hard to tune.
Since removing the air cleaner (leaning the mixture!) seems to improve performance, it sounds like something is making your mixture way too Rich. If I'm right about how these carburetors work, a power valve that's remaining open will allow fuel to flow more freely, and the carburetor will be locked in its power circuit - a temporary "enrichening" of fuel delivery that simulates larger jets upon acceleration.
The accel pump also serves this purpose to a degree and is necessary on heavier gasser vehicles, which is why I suggested backing off on the accel pump squirt a bit. It won't be a permanent solution, but it will at least verify if your tip-in condition is over-Rich or not. For my own heavy IH machinery, the 2210 seemed to never have enough enrichment to keep it running.
Keep in mind that this is related to my personal experience with these units, and I might be handing you useless information if your unit happens to be of a significantly different design. I May even be totally wrong, so here's my disclaimer: I don't know very much. This is all just me fitting together whatever information I can remember about these mixers into something that might help.
It is likely that more specific (as well as more helpful) advice from more experienced individuals could be offered if a few focused pics of the carburetor were posted, as well as your own 4-digit list number that Mike mentions is stamped into the front of the carburetor.