created a new local git repo where I copied the files into
The right move would have been to clone your fork.
I would like to change my local git repo to be a fork of the original repo and re-sign all of my commits
Actually, don't touch your current local repo.
Clone your GitHub fork repo locally (a second local repo), and rebase your commit from the first repo onto a dedicated branch:
cd second
git checkout -b myBranch
git remote add first ../first
(../first
is the relative path to the second repo local folder of your current first repo)
git fetch first.
git rebase --onto myBranch $(git rev-list --max-parents=0 first/master) first/master
(here I assume you put commits on the master branch.)
(See "How to show first commit by 'git log'?")
That will replay all your commits after the very first one of your first repo (assuming that the first commit was the one with the copied files, before you started adding your own), up to the last commit of your first repo, onto your new dedicated branch.
Push that newBranch to your fork, and you are all set.