how to adjust the derailer - apart from the L/H limiting screws
You need to loosen the screw that holds the cable and pull that cable out a little bit.

The limiter screws that you've used so far are rather used to prevent the chain from falling off, and it's a finer tuning than you appear to need now. Thus it would be useful to level them out before pulling the cable. After you adjust the cable, take a few minutes to make sure the derailleur does not throw the chain over the outer gear.