If you go with the sticky back velcro, might as well sew some on fleece cut to fit over shelves and then stick some on the bottom to hold fleece cover on shelves and be removed for cleaning. This would work for wire or wood.
Another option for doors for a more permanent set up, would be to staple the hardware net to the walls, ceiling, & floor, then use pvc tubing for a door frame like it's done for those home made cages. But the velcro & pet screening is a very good idea.
If your shelves are the wire kind, see if you can get hang bars for them, if they don't have them already, you can cover those in fleece as well and use them to hang toys from as well as attaching vines or plastic chains to hooks if you put any up.
Don't forget about floor toys, if the floor is interesting for them to explore it gives them a chance to hang around where you'll be most likely.
Have fun with your imagination, you are lucky to have a large space to make a glider room, some other's do as well, so try a search on "glider rooms" and "photos of glider rooms" that can give you good visual on ideas.