Everything was working fine until about a week or two ago. Earlier, the screen would wake when I got a notification or if I titled my phone a little, the clock would show (working normally)

Now, my phone constantly wakes about every 10 seconds. It happens even when I'm not getting any notifications, or moving my phone at all. I don't know what's going on. I'm pretty sure this is causing some battery drain. How do I turn this off?! Is there a way to fix this? I did not change any phone settings but this became a problem.

I got some advice online to go to the Moto app and turn off "Display" but that did not help. 

Start with taking a look what apps are running on the background  and close one by one to see if it solve the problem.

Start with apps that are not installed true Play (if you have those installed).

I suppose you already did try save modes.

I reset app preference and that seemed to have solved the problem! Thank you.