Leveling bathroom floor with purlins (surface shims, leveling strips)under tub
Assuming your plan is to level the entire floor area, I feel that using tapered shims with the 3/4" ply would be the best of the options presented. You will have to deal with the extra floor height. I just don't like extending tile under the tub.

Anyhoo, if you were to level backerboard you would need leveled plywood under it anyway, for support, no?