Quit using twitter for three weeks. Do it in a way that will require a password reset.
- Make sure you're comfortable with your twitter page looking the same for a long period of time.
- Post a simple tweet saying you'll be gone. Mine was
#hiatus. - Generate a random password and copy it to the clipboard. A one-liner that does it in OS X is provided at the bottom.
- Delete all GUI twitter clients from all devices. For me, this meant my MBP, my iPad, and my iPhone.
- Log out of twitter on all browsers, except one.
- Go to the password change page in settings. Paste the password in twice and save it.