Don't touch the limt screw (except maybe a tiny bit looser to improve shifting to the big ring)! One of the limitations of a compact is that, when you're cross-chained small to small, the chain will drag across the teeth of the large ring. Just don't cross-chain and you'll be fine
I can get to about the third cog from the bottom (14T) with the help of the trim before my chain drags on the large ring. I try to shift to the large ring sooner (15T or 17T), depending on cadence and terrain, but the best laid plans....