Thirteen has Electronics so he can Help, maybe cutting on the time instead of gaining advantage on the roll?
The gand could also help dissassemble the 'spare' droid with his/her Mechanichal toolkit.
She only had to use one HD so she probably did not need to take the 'Long Rest' equivalent, so with just a Short Rest I would allow her and Thirteen to work on the war droids while the rest of you were resting "more" (or more restful

It would still be a jury-rig 'limitations' though. In Saga it was +5 to the DC to jury-rig something and after a 'scene' the jury-rigged device lost whatever fixes you provided. So with one Hour of Jihahna and Thirteen would make a Tools (Mechanic) check of DC 20, with Advantage. If they succeed the restore one of the droids to 1d6 + whatever they rolled above a 15 in Hit Points. After the scene (depending) it will be broken again.