Yes, the limit screws don't change the position of the RD, they only limit the outer range of travel.

You might check the pulley clearance to the sprocket, and if it's too close in that one position tighten the "B" screw to back the RD down a hair, but that's not usually the issue. The only other adjustment is for trim, but that would affect all positions except the outer extremes.

When people have problems like yours it's often that the RD hanger is bent or mis-aligned slightly. That requires a special tool $50.00+ that checks it against the plane of the rear wheel, something that a bike shop can confirm and correct for $5-15.00 or so.

Sometimes it's not the RD at all but a slight variation in spacing of the cassette or a sprocket installed backward. Check your cassette and confirm that all the shift gates or cutouts are on the outside, and improvise a feeler gauge using a hex key or something else to confirm that the space between each of the sprockets is identical. If it isn't, you can increase spacing between anjacent sprockets using a paper shim soaked in oil.