Covering a creepy old tile ceiling
Depends on the kind of ceiling tiles. My inspector told me that the ones in my place are a variety that would indeed let me screw drywall in place directly over them. That isn't going to be true of all types, and I don't know how to tell what type one has just by looking.

(I too have a mix of ceiling heights, but that is because the house was built in two stages 50 years apart and the conventions differed. There is an area where the renovations overlapped the old house and the ceiling was lowered, admittedly; basically just the dining room and part of the kitchen.)