So, I got just as much attention and help from the front line technical support as I expected. Here's the issue: WTNH has some kind of encoding issue on the DirecTV side that's been happening on and off over the past month or more. It looks like the frame rate is too low or something. I've checked it personally with a neighbor who has Cox cable and I didn't see it there (WTNH also says they don't see any problems). This is definitely a problem on DirecTV's side.
This is the only channel with this problem and all receivers are affected on different HDTVs.
I was told this issue was moved to the next level tech support (who will run some tests on my equipment), but I don't feel confident that the right people have been contacted.
Is there a better contact avenue with such a problem?