While up on the lifts, I swapped out the front and rear diff fluid as well. I used my superior negotiating (whining) skills and got them to throw in the fluid swap for free as long as I provided the juice. Went with your suggestion of Royal Purple, which, by weight must be made of gold.
You know, I have not really felt much difference cornering at all. The only change I think I feel is on bumps. Small bumps with a steep drop (like a speed bump) might seem a bit harsher - like the rear is pushing down to get the tires on the ground. Big bumps seem smoother. But - I think this is how it is supposed to work!
I put 600 miles highway, offroad, and city this weekend on the new lift and really could not tell you that I ever really felt any difference from stock.