Neck dive has a lot to do with the strap. I've watched Don Felder goes hands-free without dive in spite of 18 tuning keys....no dive on my 2016 Gibson SG with "Green Keys. "
I like the mini-Grover tuners on that guitar. Personally I don't own a 12-string guitar but have played one in the past. They are very rich sounding and sparkling in tone.