I alternate my mixed grip, even within the set. Works very well for me.
You'd probably just have to get used to it.
i find that the hook grip works wonders
Deadhangs on a finger board are great at increasing grip strength. I climb 2-3 times a week... Started with a 60 second hang on a bar, progressed to finger hangs of 30 seconds. Peg boards and inclined line boards and great as well.
Still, nothing beats a good climb, in the Toronto area The Toronto Climbing Academy has good facillities
I used to climb before I took a nasty fall. Perhaps I'll pull out my finger board.