Don't clip anything off of anything. You did not mention your popoff specs. Changing your spring tension, and thus your pop-off, w/o knowing what your pop-off is, would be a mistake.
How do you know it is lean hesitation? It could be rich. You didn't mention your pop-off spec, which is very important. A leaking needle and seat will dribble fuel into the carb making it rich in the low speed. You must verify it is working correctly. If you haven't had the fuel pump side apart recently, you need to check that as well.
Pop-off should be set at spec. You don't much need to fine tune your pop-off if it isn't leaking. 50 or 55 makes little difference (as long as it is the same for dual carbs). The low speed jet and the pop-off work together to create the low speed mix. You can make up for a higher pop off with a larger pilot jet and vice versa. Don't alter your popoff just because. Set it to what it should be and tune the jets.
I realize mikuni says that your low speed screw is to adjust a smooth idle. I don't agree with this thinking. The jets only come in 2.5 size increments. You can buy a 145 or a 147.5, but nothing in between. I like to think of the adjustment screws to fine tube b/t jet sizes. You use your screw to make that 145 jet work in the range of 143.75-146.25. A set screw at 1.5 turns out is a 145 jet, 3 turns out is a 146.25, and all the way in is 143.75. This maxes out your effective range of the jet, and if you can't get it tuned w/in the 3-turn range, you need to change jets or find the real problem. Yes, the screw is important to the idle, but you can also change the idle with the idle set screw. I have had lean hesitation off idle with an absolutely perfect feeling idle (I haven't been tuning with a tach). I richened my low speed screw and turned down my idle. The result was an unchanged idle, but no more lean hesitation.
Don't think of a part of a carb affecting only one part of the running range. They all overlap, and changing one changes another. You tune the carb as a unit, not the jets individually.
Fuel tanks do not need pressure to run. My X2 never had pressure but it ran great. It never had any lean or rich hesitation. Actually, the motor really changed performance when I modified the hood to get more air, but still, my throttle was responsive and my plugs were perfect in color. A motor may run it's peak with the right pressure in the tank, but it will run with no pressure. As long as there is not a vacuum, it will run okay.
Check your pop-off, make sure it is at spec. Verify you are lean and not rich. If unsure, go up a jet size and decide better or worse. I hate to tell you this, but you might have to spend $30 buying a few jets you don't end up needing once it's tuned.
