Clear or reset my lock screen password/PIN
I got it fixed. Here are the steps I took:


Use the exploit here entitled "Phone: Use a hole to disable your lock". For me, it didn't work exactly as documented, though. I had to mash the password keys for a long time (calling my phone was unnecessary), then swipe up Google Now, mash the password a few more times, and hit Enter. With that, Google Now pops up and the phone is unlocked. I didn't test to find out how much of this is necessary and how much isn't.
Fire up a terminal app on the phone. I can't get root access from adb. Type su to become root. It should go without saying that this method will not work unless the phone has been rooted.
Enter the following commands to clear the password (source). Each line represents a command to type, one at a time.

sqlite3 /data/data/com.android.providers.settings/databases/settings.db
delete from secure where name='lockscreen.password_type';
delete from secure where name='lockscreen.password_salt';
.exit


Tip: These commands will be easier to type if you use Hacker's Keyboard and type with the phone in landscape orientation.
Reboot the phone.
The screen will still be locked and non-unlockable. So, repeat step 1 to unlock it.
Go to the security screen and hit Screen lock. You will be asked to confirm your PIN. The new password is null. That means that instead of entering a password, just hit Next with a blank password.
Now, you're in, so go ahead and change your PIN to whatever you want.