Nut slot depth is always set for clearance over the first fret. I've never heard of anyone addressing neck twist by changing nut height. That's a recipe for poor lower fret intonation, buzzing, or excessive force needed to play in the lower positions.
This sounds like the "fix" has got off on a bad start, so I'd cut my loses if it can be exchanged at the dealer level.
You'll quickly get used to a new instrument. Dana builds so his guitars sound good out of the chute.
"Neck twist" is highly overblown as a source of intonation difficulty. Except in extreme cases it can usually be remediated by a slight shift in the saddle stopping point. If you have twist in combination with a truss rod that can't correct the relief then it's a problem.
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