[14u2c]

I have to go, you may be better of installing new cans? If you have access from above, use New construction cans, NOT remodel cans, this way ceiling will help support., screw in cross braces.
Back later

How would you be able to hammer the nail or screw the screws in with a new work can? If there's a attic up there you can do this but by the looks of it I would say that's no attic..

[Stratmando]

I never got an answer about an attic or not, that's why I said If there is an attic, new construction cans may be a solution. And will help support the can.

[Stratmando]

14u2c, Just to answer your question, poster said they will remove insulation when they are up there(attic?)
Just did a remodel, drywall is already up, and I used New Work(not remodel), they cost less and are more secure if you don't mind working in the attic for a secure can.

[creahands]

If he can get into attic, he can wedge a 2x4 between ceiling beams and screw the pot into that. This would be a permanent install.

Chuck

[KISS]

Mmm. Can't offer anything for the cans, but.

There is a construction adhesive (Liquid nails) remover available, other that that, sand.