Seems to me that Israel should publicly offer to cede the Gaza Strip to Egypt, just like Israel ceded the Sinai Peninsula to Egypt. If Egypt says no, then Israel will have a much freer hand to impose order on Gaza. If Egypt says yes, then Egypt will become responsible for doing that.
There would have to be some agreement that Egypt wouldn't just spin off Gaza into an independent or autonomous country. Everyone would be better off if Gaza were no longer a free agent. And that includes the people of Gaza.