Locking tuners will help greatly and a quality nut(cut well and of good material/mabey lubed...not plastic).If you use the trem to dive,make sure to tug up a little on the return.The springs in the back of the guitar attaching the tremolo to the claw also make a difference.You may need more tension(more springs)or less(alternatley)...just fiddle until you get a stability your happy with.

If you do anything to increase stability,I would say get a good nut replacment first.Its generally cheap and will improve overall play/tone/stability greatly(I used a graphtec on my old fixed brige ESP and it stayed in tune well...much better than the stock nut).