+1 on a non-factory replacement bed
If you have a garage with open rafters or maybe a handy big and strong tree limb, you can lift the bed off with one of those hand ratchet winches ("come-alongs"). Just rig up some sort of multiple point attachment that pulls evenly.
With a fleetside/wideside bed, I just cut a couple heavy boards long enough to catch under the pickup bed flanges, and ran chains around those boards. Of course, when I did it, I had access to and used a forklift
It might be handy to rent/borrow a flatbed trailer or two to shift the beds around. Hoist the bed off your p/u as suggested above, pull your p/u out from under, and back a trailer under the airborne bed for removal. Reverse process for the new bed.
Or you could just leave the old p/u bed hanging in a tree for artistic value