Covering with the stabilizers already installed is not too bad. A lot of folks do it that way anyhow. Just cut a small strip of covering for the angle where the pieces meet, and iron it in place. Then cover the rest of the surface.

As for the hinges, I prefer to cut the control surfaces off, cover everything, and then install new hinges. Some people cover after they hinge. It partly depends on the type of hinges. If they are CA hinges, they are easy enough to cut off and install new ones. If they are pinned hinges or Robarts, it's a little harder to re-hinge, but I would still rather reinstall the hinges than try to get the covering in between them.

On a trainer, they are most likely CA hinges. I would just cut them off and install new ones.

Good luck.