I do the broomstick trick when the hide I want is towards the bottom. Grab a wide bottom broomstick and slide it on top of the hide you want, then with the broomstick lift and take the weight off that hide so that you or a work friend can slide the hide that you want out. Usually works well and saves time unloading then loading hides back on the horse.

I find steam to be helpful taking off glued covers

How about hidem binding? Don't always use it but it does create a nice finished look and hides all the staples