@GustavinoBevilacqua lessons learned:
1. Hammer the wire until it is as thin as possible
2. Make the cuts deep and narrow
I was not hammering enough and the wire was somewhat rounded. Because of this I was making wide cuts to fit the inlay, and it bounced around. Because of this I had to use a lot of glue. Lots of hammering. The whole thing was, to say the least, messy.
With thin wire, the sides of the narrow cut grip the wire. It just requires a little glue to keep together!