The fact the Drywall isn't flammable has to be a concern.

I finished my basement myself and used drywall on the ceiling. All I
used were 8 Eye Bolts and 2 pieces of 2 x 4.

Cut 2 lenghts of 2 x 4's just longer the 4' so you can screw an eye
bolt in either and fit the drywall in between, like so:

0 0
| |
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Screw the other 4 eye bolts into the rafters where you want to place
the drywall. I then used 4 nylon strap (the kind with the rachet
tightener) to hoist the drywall into place. Use another 2 x 4 to
press it hard against the ceiling.

When I say I did the ceiling myself, I mean I didn't have anyone else
in the room.

Chuck