Got it off last night.
I used a scalpel to probe lightly under the nut and where it joins at the sides.
taped up the fretboard next to it, put a small block of wood on the fret side, and tapped towards the headstock.
It came off easily.
You can see it isn't solid. I don't know if other nuts are solid. I would think it would be more stable and have a stronger glue join if it were.
I'm going to clean up the join. Sand down the base in stages for a lower action and try to get a cleaner join.
I'll show progress.

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