Limit screws are often misunderstood by folks not familiar with derailleurs. They don't actually control the movement of the derailleur, they only establish the inner and outer range of travel possible. It's the cable itself that controls the derailleur movement.

I think some of the confusion occurs because in the slack cable position (usually the inner front & outer rear) the derailleur will be leaning on the limit and so it does control the position. In the opposite positions, (outer front or inner rear) the position is controlled by the cable adjustment, and the limit screw serves only to keep the derailleur from going beyond the desired position.

I always set the tight cable limit independent of the control levers,, activating the derailleur by pulling the cable away from the frame tube like a bow string, and setting the limit for optimum shifting to the largest sprocket. Once the limit is set I then adjust all the shifting and trim by cable tension.

Unfortunately many bikes today have no barrel adjuster to set FD cable tension or trim, which makes what used to be a simple 2 second job into a trial and error nuisance. To overcome this I suggest adding an inline cable adjuster, so simple stays simple.