So I could have RMA'ed the device through Samsung and have them repair it. I thought about that, but then decided that this process would probably take weeks, leaving me without use of the device during that period. I decided instead before sending it out to Samsung to crack the case carefully and see if I could see anything simple that might fix the issue.
I started by flipping the device over and prying off the rubber feet covering the two screws closest to the hinge with a small flat head screwdriver. If you pry carefully on the rubber feet they will stick back on just fine. Then I started to unscrew those screws. I noticed something though as I was loosening them. They were already pretty loose. So on a hunch I tightened them up and like magic the screen was now held firmly in place at all angles. Basically, I think that these screws are supposed to clamp down on the hinge mechanism somehow to keep it tight and since they were loose it allowed some slop in the hinge.
Clickable thumbs to images showing the screws that I tightened.
The only tools used for this fix were
- small flat head screwdriver
- small phillips head screwdriver
And by small I mean like small enough to use on the screws in eyeglasses. Also, from memory I do not believe these screws had any thread locker on them which may have prevented them from backing out. I did not think to put any on when I was working on it, but if they come loose again I will put some on the threads. Happy fixing!