I've recently run into the grip strength issue (haven't been rock climbing like I should be) and the alternating grip has worked well. Yesterday I hurt my wrist and I need to RDL today, so I went out and bought straps for the first time - will see how that goes.
At the retreat, Chad Waterbury gave us an exotic exercise that will help with DL grip (among other things). Here is the illustrated description:

DL a bar that is lighter than your normal DL weight.

Walk appx 4 or 5 steps to a bench you have set up.

Place the bar down on the bench for a brief second, readjust your grip, and walk carefully backwards to your starting position. Lower bar back down.