Haha, I did a job along side a tiler one day who wondered how I was going to pull the tub out and replace it in an installation setting like the one you described, he went on to tell me that he did something similar in his home and that he chopped out all of the wall studs to be able to pull out the tub. My jaw dropped at that story, as I showed him that all he had to do was to move the tub out a little bit so that the apron was no longer resting against a wall stud, but was instead in the void between wall studs. Then all he he had to do was lift the tub up a little so that the bottom of the apron cleared the sill plate, and then just angle the tub up and out of there! He was pretty amazed at how simple it was, and I could tell by his face, he was a little bit upset.
Do not expect to get this done in one shot, especially if you plan on doing a mortar bed...dry fit, dry fit, dry fit!!!!!