Here is what worked for me (and apparently for others, from other forums):
1. Hit Power to turn off the DVR (you can use the remote)
2. Hit Menu to enter the DVR's setup mode
3. Select anything other than 1080i (I used 480p, but I don't think that it matters).
4. Hit Power to exit the setup mode
5. Hit Power to turn on the DVR
6. After a few seconds (I wait 15 or so, just to be sure), power off again
7. Go into Menu again and reset it back to 1080i
8. Power off
9. Power on.
This stops the stuttering. I don't know if there is a bug on startup or what, but this has to be done anytime the 3416 reboots. Which, I think, it does more often than I realize (middle-of-the-night chokes, and all).