I have tried clicking the sync button for "Sync retired projects" and every time I reload the page, it says that my username for those projects is still an old one and not my current one. My goal is to get my current username to show up for the "My detailed stats" page, even though my new username is set for this profile, the "My detailed stats" page shows my old username.

I'm assuming that was the account name used at the time the project(s) were marked "retired"? You might have to temporarily change your name back, try the sync, then change your name back?