Rubberduck,
Nope, no better way than what you pointed out.

You'll need to go to the LHS and pick up some more CA hinges. Cut the old hinges off. Use an x-acto knive to cut new hinge slots next to the old ones. Then insert the new hinges and re-glue them.

I know it seems like a disastor, but take a deep breath and relax, it's not a big deal at all.

Hope this helps