In my experience, this solves the sticky 301 issue and you should have no issues with cached 301s anymore.
Works perfect for these kind of investigations or if you made a mistake during site development.
(Fingerprint usage: have https://myfingerprint.example.com 301 to https://myfingerprint.example.com/unique_id_3b136c1cb, then embed https://myfingerprint.example.com in an iframe and see which request is made.)
I still never use 301s for that reason. Things may have changed, but I dare not try!
I use 301 for http:->https: redirects because (a) I doubt we're going back, (b) it prevents some cleartext leaks (like the Host header), and (c) it is slightly cheaper.
> we never figured out how to get the browser to re-learn the responses for those pages without drastic measures.
If you control the target URL it is easy, just redirect back. Seriously: The browser won't loop, it'll just fetch the content again and now not seeing a 301 will forget that nonsense ever happened. This is why 301 is usually a fine default for same-site redirects, or if the redirect target is encoded in the URL (such as in tracking URLs).
The big no-no is don't 301 to a URL you can't control unless you have the appropriate Cache-Control headers on the redirect.
