Mike that is absolutely without a doubt one of the worst nuts I've seen.
I can assure you that the person knew nothing about nuts.
Use a razor knife and scribe (very neatly) around the nut before trying to remove it.
Tape off the fretboard to first fret - wrap around neck to protect fretboard edge.
When you jar the nut trying to break loose any glue go easy. If the top of the nut breaks
at six and first sting (to the slots) no loss.
The idea is to break the bond with strong enough taps and soft enough it doesn't break
the wood.
You'll be directing the blow as if to slide the nut out so make sure you cut all the edges
so when it does it will lesson the chances of taking finish, neck and fretboard wood with it.
Any little wood it takes from the slot is not such a big deal.
And one more thing....one didn't need a gauge for that nut! Nothing about it is even close! LOL