I've shifted badly seized caliper pistons using the hydraulics themselves. Put a hardwood block between two opposite pistons fit a clamp over one of the other pistons and use the hydraulics to force the last piston out. Clean and refit the piston and rearrange the clamp etc to do the other three.
When the pistons are merely stuck, compressed air from a bicycle stirrup pump will do the job.
Hope mountain bike callipers have screw on caps (similar to Yamaha Blue spots) but the Hope calliper is a one-piece and the screw caps only access the outer pistons. Even then you'd have to drill tap and pull them out. The clamp method works on all four pistons.