Garage door closes and then reopens - Already adjusted force sensor to max and tried adjusting cable tension
This was a case that fell under General Knowledge idiocy. I had found the Down Power screws and was treating them like the Down Limit screws. In actuality, both generally need to be adjusted.

My method for fixing the problem (in case others find themselves in this situation):


Clear out debris under the door (this has been a problem in the past. A plant or some dirt will be under where the door is, not enough to trigger the electronic eye sensor, but enough to bounce the safety sensor)
Ensure that the electronic eye sensors are cleared (this usually manifests itself as the door not closing at all, just clicking, but just in case)
Adjust the Down Limit screw (located on the left side of the unit when looking at the garage door from the rear) a quarter turn counter-clockwise.
If necessary, adjust the Down Force a bit clockwise to ensure the door goes all the way down now.