>I do not know if GitLab does anything different; I've never used it in anger. I'd bet $10 the answer is "no, it's basically just the same as GitHub", though.

You would bet incorrectly then. GitLab does essentially what you're describing, the only difference being that it compares different iterations of the force-push "naively", so if your force-push includes for example a rebase onto master because another MR has been merged ahead of yours, the diff will include the changes that have been rebased onto.

If you decide to register an account on GitLab, simulate the MR and prove to yourself that ~90% of your interdiff post has been implemented by GitLab for about a decade, kindly donate the $10 to your nearest homeless shelter.