The problem I have is the walls from top to bottom aren't exactly
plumb/square, and to get the wall square means either replastering
the wall square (and then waiting 1-2 months for it to dry - correct
me if I'm wrong),
OR making up the gap with the tile adhesive.

Why not plaster the wall flat with the mortar (instead of bonding plaster),
let it set for a couple of days and then use proper waterproof adhesive for
the tiles?

Christian.