If you don't want to require an alternate email, or security question(s), or a SMS/cell phone number from the user on signup then you'll be stuck with users that have orphaned accounts.
Here's something you could try, but users will still forget to print it out or not care.
- When a user signs up, give them a one time use "secret token" (basically a serial number)
- Tell them to print it out and keep it safe
- Allow them to use the "secret token" to reset their email address
- Once they verify their new email address, remove the old "secret token" and send them a new one