Tearing out the existing ceiling is a minor expense, but very dusty! The real cost is the replacement. I doubt you can pick up 6 inches in height. A drywall ceiling is usually put up as high as possible.
Leave the ceiling as is and do your renovation.
and it took me 4 years to do it all. Anyway
what I did with the ceiling is put 2x2 suspened ceiling with recessed lightings between the joists. Most of the height is 7 feet and 5 inches. Small area has the height
of 6 feet 8 inches. I have been very please
with it since there were time when I need
to do some plumbering, electrical, etcs work.
It was nice to just take out the panels then
put it back. Yes, the cost high BUT looks