I have used one of these "universal" sockets with eye hooks. You have to start them a half-turn or so, but then it will spin them right in.

You just need the typical socket adapter to use it with a screw gun.

I've never used that drop-ceiling tool, but if it would grab them snugly enough that would be ideal as you could use it to start the things, too.

Good luck.

Universal - Smart Socket Wrench / Tool Set w/ Ratchet and Extension:Amazon:Home Improvement