I just googled that model. I really like that little cutaway. Unique. I've never seen it on an acoustic (and only ever on the back on electrics).
You might still want to consider some of those humidifiers but use them opposite of the recommended method. They typically contain a sort of sponge that needs to be soaked prior to being inserted into the instrument. Rather than soaking them put it in dry and it should absorb some of the humidity and need to be squeezed out every few days.
How does other wooden furniture in your home handle the climate? The guitar should be similar.
Those specialized files are intended for making your own nut. That's not anything you should be needing to do. But if you insist on getting some, a cheaper alternative would be hobby / modeling files similar to these -
https://www.amazon.ca/AFUNTA-Hardene...ERPBCRSXKR5WF5
Most of the rest you describe sounds pretty normal. 3mm at the 12th is about what mine has. It's also higher at the bridge. And when I check - which I msspoke last night - rather than pressing at the 1st and 12 (for an electric), use 1st and last with an acoustic.
And generally speaking you're not playing that high on the neck on an acoustic. And if you are, anchor the string with your index finger and fret with the others.