You don't want to turn the limit screws to adjust the derailleurs. These limit the total distance that your derailleur can move. They are for preventing the derailleur to move too far and pull the chain completely off the gears.

What you want to adjust is the barrel adjustment. I had something similar in that I am mostly on the middle chain ring on my hybrid and when in the top gears in the rear, the chain rubbed a little bit on the front derailleur. Since if I ever use smaller gears I just go to the small ring, I gave just a quarter turn on the barrel adjustment on the front derailleur and that moved the derailleur just enough to no longer rub when I was in higher gears in the 2nd chain ring.