I was about to write my own tool for this but then I discovered:
git diff --color-moved=dimmed-zebra
That shows a lot of code that was properly moved/copied in gray (even if it's an insertion). So gray stuff exactly matches something that was there before. Can also be enabled by default in the git config.
I used autochrome[0] for Clojure code to do this. (I also made some improvements to show added/removed comments, top-level form moves, and within-string/within-comment edits the way GitHub does.)
At first I didn't like the color scheme and replaced it with something prettier, but then I discovered it's actually nice to have it kinda ugly, makes it easier to detect the diffs.
That's a great solution and I'm adding it to my fallback. But also, people might be interested in diff-so-fancy[0]. I also like using batcat as a pager.