Well, went to Sprint store last night. Drove past 4-5 independent stores to get to the corporate store in my area (NJ), only to be told that they don't do repairs, but maybe the independantly-owned stores do. Now that I think about it, they never even asked if I was on the Protection Plan or not...
Also called Samsung. They'll fix it for $180 (seems a bit steep), but claim a 5-7 day turnaround (not incl. shipping).
As for Sprint's TEP, looking at Sprint's website, besides the monthly fee, there's currently a $150 deductible for the S3 on top of the $11/mo TEP. Glad I opted out. The money I've saved since switching to Sprint by not paying for the TEP more than covers an occasional repair or replacement.
I can't see the video linked above from here at work, but if it's a guy replacing the screen, I'll need to check it out. Amazon has a replacement glass for $24.
Edit - Well, I was finally able to watch the video. In the comments of the video posted above. In the video's comments, the guy has a link to another video showing why you can't just change the glass for $20. The Samsung repair is looking like the better option at this point (not much more than the part needed). Now I just have to get my hands on a phone to use for 2 weeks while Samsung has it...