Guess I'm gonna have to move ALL of my coin to paper wallets. Seems like Coinbase is no longer safe even for the tiniest bit of coin I had on there.
Wait... You didn't realize someone who could guess your e-mail address could send a password reset request?
Look, careful planning and use of multiple wallets to improve security, including paper wallets or other offline wallets is smart.
Right now, I do believe your priority should be to make sure your EMAIL account has 2-factor authentication enabled, and that you are using a SECURE e-mail provider, not one like Apple, that might allow someone else to reset your email account creds by making a phone call or otherwise social-engineering support.
I would suggest booting from a bootable Linux CD (to sidestep, just in case of PC-based malware), log into your CB and E-mail account, and carefully go over your security questions.
Make sure none of the security questions are guessable.
MAYBE change them all (write down and vault the new answers), for good measure.