Why not just use the hydraulics to pump the pistons out before disconnecting the brake lines?
The pistons don't come out far enough with the disc (or anything) preventing them from coming almost all the way out.
This is how I always do it now. If it is a two piston and one wants to come out before the other I let it come almost all the way out and then block it with a piece of wood or anything else I have laying around then I will pump the other one out till I get them both out.
Grease seems like it would have to work, but be a big mess?
I've found compressed air to work, you gotta be careful not to shoot
the first one that comes loose across the room...
When I just want to push the pistons out far enough to clean them when
installing new pads, I've finally gotten up enough nerve to use hydraulic
pressure. I haven't squirted a piston and a caliper's worth of fluid out
on the ground yet

...
Here's some pistons starting to come out with air and blocked by a
board.

-Mike