Pull them down or use a white painted screw head and strategically place the screws in a incon place and work that way.
I guess, by your post that they are still in place but only by the contingent tiles holding them there. Consider shooting some glue or adhesive between the tile and the ceiling via a horse medical needle, or a basting needle.
Carefull cut out with a sharp box knife a small circle and then apply some glue then re insert the circle.
Go up in the attic and screw dry wall screws down from the attic into the areas and then from below, cut the screw points and paint white.
Many things that can be done other than ripping down the ceiling.