This works for me to keep the CCF in place. Lay the pad in the hammock at the diagonal / asymmetric position you prefer, then draw a line down it's length along the centerline of the HH. Now glue or stitch a piece of webbing to the pad's bottom (under your mark) with a loop or "D" ring at each end. Tie a cord, with a clip or micro carabiner at one end, using a tautline hitch, to the ridge line at the head end where it meets the hammock. At the foot end do the same thing using a bungee cord. To use, attach the pad to the lines at both ends, using the tautlines to adjust it's position. The bungee allows you to push the pad aside to enter and it "pops" it back in place when you get in.
One technique to get in your bag is to sit in the HH slit, pull the bag over your feet, stand up (on something like your sit pad, pull the bag up, and lay back into the HH. Personally, I find a quilt best, with a bag I'm always wrestling with it to enter and work the zipper.
Hope this helps,