Originally Posted by FBinNY

I think you don't understand what the limit screws do.

Imagine you need to park your car between two others at the curb. The position of those cars determines how much room you have to move back and forth. If you move either car forward or back slightly, it'll affect how far your car has more or less room to move in that direction, but your car won't actually move there until you move it.

Likewise the limits. They determine how far the derailleur can move, but it's the cable movement (not tension) that moves it.

Applying that, if you want to move the derailleur farther out in high, you have to back off the limit a bit to make the room, then adjust (sighten/shorten) the cable to move the derailleur out.