Since you have a slot cutter rehinging is not that difficult either. ( assuming it's electric ).

Carefully cut the existing hinges to separate the control surface.

Cut off any remaining hinge material. I also will use a drum sander to make the remaining material flush with the wood or covering.

Now you have to make a choice.

You can carefully try to cut new slots immediately above the existing hinges. The offset will be so small that it will not matter.
Ideally you would cut the existing material out, but this is almost impossible. Just manually scribe a small line or depression where the slot cutter will begin cutting, and then use that as a guide.


OR you could slot new hinges adjacent to the area they are currently in.


Normally I do the former for looks.

That's it.