I would actually just go with 3/4″ (minimum 5/8″) and allow the backerboard meet the tub deck. this will make it easier to waterproof and make it so that you don’t have to fill the tub gap between backer and flange
Simply apply the poly sealant to tub deck before sliding panels down
Check with a level on the studs and an see if they are all inline with one another.
I’m thinking that narrowing down the furring size will leave that middle stud set behind the others. The walls are probable just out of square, and a 1/4″ really won’t be noticed, but a non-straight or bowing wall will cause difficulties with tiling