The H screw is turned almost all the way in to keep the chain from slipping off the big chainring. The thing is shifting fine this way, but is this level of adjustment masking an underlying issue?

If it matters: 22/32/42 & 11-34 cassette. All combinations work well except 42x 34 & 26. 22x 11-34 works without noise

FWIW I've often nearly bottomed out one limit screw while the other was quite high. Everything worked fine.

There are manufacturing tolerances in the way the chainring and the derailleur are attached. There's a lot of parts in a derailleur so a lot of tolerances. Or, something could be a little bent.

The combinations that don't work well probably would if you got a longer cage derailleur and longer chain. Not that you want to use 42/34; it's better to have a shorter derailleur. I don't think limit screws are the issue.

If it's shifting fine, you're good. The limit screws on a front derailleur have to work with a range of chainlines (distance from the bike's centerline) on different bikes. Maybe your particular crank & spindle happens to put your chainline near one end of that range.

The big thing with front der limit screws that are at their limits is that the der's swing and resulting cage position, WRT the rings, can be at the limits of working relationships. As the frt der cage goes through it's swing it moves both in and out (which the limit screws directly control) and also moves up and down. So the gaps between the cage's bottom edges (or the various sculpting of the cage plates) will raise and drop as the cage moves in and out. When the cage's side to side movement is at one end of it's travel (as when the rings are far from the frame) this vertical component of the cage swing is greater, conversely when the cage moves through it's inward portion the vertical component is usually less.

This results in a non linier response to lever travel and cage/chain displacement. Changing the ring's distance from the frame can affect the der's ability to shift. But this too has limits. Andy.