How can I replace ceiling gypsum board and loose fill insulation at the same time?
Hoisting the insulation with the drywall panel is a bad idea. I would instead install fiberglass bat insulation between the joists. You could use the kind that is faced with paper and staple it to the joists for added support. If just plain batts are used then you may need to add some type of staple on stripping to help hold the batts in place. Install all of this except for one small area where you can go up and put in more of the loose insulation above the fiberglass if that is desired or needed. Finally close off the small area by pushing up an oversized bat that covers the opening from above and then install the final piece. If using the paper backed staple that in place. If the ceiling previously had some type of vapor barrier you need to install similar material on the bottom of the ceiling joists. 

Now you would be ready to install the new ceiling drywall.