If you are going to have a shower above the tub, then it makes sense to strip the alcove to the studs up to shower head height. That will let you install a waterproof tile backer and tie it into the tub properly. And it's best practice to have the tile wider than the tub, so that there is a leg of tile that goes down to the floor. In which case you can afford to remove drywall a couple inches wider than the tub width.
In that case, this may work: bring the tub in vertical, I think it will be better to have the drain end down. Arrange the tub so that tilting it down 90 degrees gets it into final position. As you tilt it down, the diagonal of the apron will be longer than 60", so you'll need to have an empty stud bay to accommodate that, possibly using that extra width of drywall removal. Also, the tub design needs to leave sufficient empty volume below the deck at the end that is on top when it's vertical, so that only the apron exceeds 60" horizontally at any point during the tilt.
Another option, if you can bring it through a door in its final orientation, is to remove all the drywall (and possibly door trim) below, say 24" AFF as needed to just slide it into place.
Cheers, Wayne