I have an unregistered account which I used on MO, and my only connection was via cookies. However, now when I come to the site it doesn't recognize me. Is there any way to recover access to my account? I prefer not to register.
I suspect not without registering. You may want to create an account and then ask a question on the new meta with the "feature-request" (or even "bug") tag explaining what you want.
I doubt it's technically impossible for them to copy over the old cookies, but I rather suspect it would be a lot of work!