Tips for re-hanging fabric?

I’m planning a project which will be half on the machine, half off the machine. The large swaths of stockinette will be done on the machine, while the more fiddly manipulated stitches will be done by hand.

I’ve always had trouble re-hanging work on the machine. I feel like I can never get in there easily enough and end up dropping stitches all over the place. Any tips or suggestions?