...okay, you guys are going to love the solution to this one. I downloaded one of the 720p versions to test it out, and the results looked a little bit more like they were supposed to, but the playback was still mostly solid-colored. So I thought about it for a second...and then I remembered a certain Launcher flag. I've always had "Disable scale-to-window for movies" selected, since the retail .ogg conversions are grainy to begin with; I didn't want them to look even worse than they had to by default. So, as it turns out, instead of the 1080p versions playing back completely "solid-colored"...
...I'd simply been seeing an extremely-zoomed in view of the center of each video.
...yeah.

So if anyone else out there forgot they had that flag selected, flip it off, and everything should work out fine. Even when they're playing right, the 1080p versions still lag the hell out of my system, and they're much bigger than my monitor requires anyway, so 720p is definitely the way to go for me. Thanks a ton, mjn.mixael.

(I still can't play even the 720p versions outside of the game, so I'll have to figure out what's going on there. At least they work where they need to, though.)