Be sure your TV's are set to "Dot by Dot" or "Just Scan" or what ever your particular TV manufacture calls the mode.
Also disable 480i and 480p checkbox options on your receivers to prevent accidentally winding up on them.
Check out a 1080P PPV and see how that looks.
I really appreciate all the comments here to help figure this out. You and several others mentioned the resolution checkbox options; the installer ended up leaving it with only 1080i checked, but when I called D* tech support, they told me to check everything from 480i to 1080i, which I did. But I haven't seen any difference in picture quality between those two combinations of settings. (When I try to enable 1080p, the video won't pass through my Denon AVR-3808CI AVR; I always had the same problem with the Dish 722 as well, when trying their 1080p PPV channel. So for some reason, my Denon hasn't been able to pass 1080p on from either the Dish or D* receivers. Although I have no problem passing through 1080p from my OPPO blu-ray player... Figured the Denon probably needs a firmware update, which I've avoided so far, given their reputation for bricking up during the update...)
But with those settings checked on the HR34 (480i, 480p, 720p, and 1080i), I've tried using that "format" button on the remote, but each time I go through that, it'll scroll through the 480 settings OK, but then the screen goes black when it tries to go back to 1080i. When that happens, I've been turning the HR34 off and on, and the picture has come back. So I'm a bit unclear at the moment how that "format" button is supposed to work. It shouldn't be trying to output 1080p, when I don't have that setting enabled in the "settings" screen, correct?... I guess what I really need to try is just connecting directly to the TV and see if it's any better.