You never rewrite published history with git. It's fine to force push signed git commits to a random branch that are going to be rewritten -- that's just how development works. But when you merge something, it stays that way. Touching history in release branches is something that will always end in tears (all of the tagging breaks, everyone's clone will complain when they update it, etc). Just bad news all around.

As for a site which cares about archiving, they can almost certainly add a tag for every commit they slurp up (making sure it doesn't get hit by the git gc). Though, I'm fairly sure that you can just configure your git instance to never garbage collect.