For me, it really depends on the song! Some songs I can tune in no time at all but end up stuck mixing it to no avail for hours (or months if I'm unlucky) or vice versa lol!!
Actually I'm doing things a little more different that I know if I was focused in doing utau covers I would achieve my covers quicker. I'm tunning at the same time I'm mixing. Basically I tunne a part of the ust, open the original song in a mixer and then open my tunned part. I compare both to understand what I want to change and then I goes back to fix it.