It's possible that setting the H limit screw to not rub in big-big combination will make it difficult to shift up in the front. What I usually do:

1. Make sure the derailleur cage is at the right height and is aligned perfectly with the big chainring.
2. With the chain in big-big combination, loosen the H screw until it starts to rub, then tighten 1/4-turn.
3. Try shifting the front down and up a few times. If it shifts okay, you're done.

If it doesn't shift okay:

1. Unscrew the H screw a bit, try shifting up and down.
2. Repeat until it shifts up easily.

Now use the cable tension adjuster to eliminate any rub in big-big:

1. Shift into big-big combination.
2. Loosen cable adjuster until rub is gone.

This method also makes it easier to shift up and down the front, as you're not pushing hard against the H limit to get the shifter on and off the "big ring" click.