If you don’t mind the nut sticking out a bit, fabricate an Allen to female Allen 7mm drill driver bit. Shorten the sleeve end first, grind to size with one side flatter than the others. Using a mini grinding stone from a dremel, flatten one side of your existing nut. Get a nice snug fit between the two. After that pour some crazy glue in, stick the bit in, quickly sprinkle pencil shavings in the joint, and then a little more crazy glue. The pencil shavings melt into a metal from the chemical reaction.
If you’re really good with tiny grinding stones, you could also create a slot on each side, without going all the way through, then either modify a high quality screwdriver, or grind an Allen key into a diamond shape.
I have used the one size bigger, or closest fractional standard, and with a little grinding hammer it in, pull it out, a few times until it’s usable without leaving in. It all depends on how damaged the nut is.
Last but not least, I wonder if an old rg rod of the same scale would fit. Find yourself a beat up, parts only guitar.