Lots of good advice so far. Adjust the ROM for maximum tension, make grip a non-issue by using straps and/or not wrapping the thumb around, and pre-exhaust the lats with a pullover variation (straight-arm pulldowns with a rope handle are a wicked choice).
I'm 6'2" and pretty much whenever I do pulldowns, I don't sit on the seat, I "kneel tall" on the ground right behind the seat for get a much better stretch at the top without the weights resting on the stack.
But definitely play around with straight-arm pulldowns as the first exercise if you want to pre-exhaust the lats so they get fully worked before the arms can contribute too much. I'll sometimes start things with 2-3x8-12, going by feel. The worse the burn at the end of the set, the better.
It's the first exercise shown by our very own Mighty Stu here.
I believe he's said they're a staple in his routine.
Jimmy Smith had a pretty good article with a bunch of tall guy training tips a while back (hehe. Back.):