I would like to preserve my current branch's history, but add a new commit which changes the state of the branch to match another branch — essentially overwriting or resetting the files in my current working directory to the state they have in the other branch, so that I can then create a new commit. How do I do this?
I can't do a cherry-pick because that would try to apply the diff between the specified commit and it's parent onto the current HEAD.
Instead of thinking about 'resetting' your working directory to the state of some other branch/commit, you only need to create a diff between your current branch and the target branch, then apply the diff.
You can do this in a single porcelain command, when on the branch you want to append the commit onto and in the top-level directory of that repository, with git checkout --patch SHA-or-branch-name .
Then choose which hunks to apply or not apply, and do a git commit.
Alternatively, apply all hunks with git diff SHA-or-branch-name | git apply - and commit it.