Put your stirrups in the highest hole and ride upright like a jockey (frog position). Learn how to ask for forward, change direction and stop without falling. When you can do that at the walk, add in some trotting and do the same - forward, direction change, stop - but also add transitions, up and down. When you can do all THAT, do the same at the canter. Then canter around for as long as you and your horse can manage. Post the trot at beats (stay up for 2 beats, down for 1 and so on). Post the canter (each stride is either you going up or coming down). If you can get your horse to walk/trot/canter and maintain cadence, move your arms around, up, down, forward, back, bend over forward, lean back, touch your toes. Basically move your arms and upper body around and force yourself to remain balanced.
This will improve your balance and improve your ability to maintain your balance should your horse do something unexpected. It will in turn make you rely less on your hands and let you release without leaning.
It's HARD and will take MONTHS to perfect but once you get it down your allover riding skill will improve heaps!