HDCP has been around for about 10 years. It was optional with DVI connections and HDMI always uses it. It's just a point to point encryption scheme.
How does the DVR behave connected directly to the Kuro? I would first see how things work connecting the DVR directly to the TV. Using a "box" between the source and the TV is really 2 HDMI connections. One for the source to the "box" and one for the "box" to the TV.
Having the DVR set to "native" is probably the best setting, but it also cause different different video formats (480i, 720p, 1080i, 1080p) to be sent to the Kuro. So if you change channels and the new channel is a different video timing/format then it will take a few seconds or so for the TV to sync. And this would be without the AVR in between which could cause additional delays - 10 seconds is a long time.
And the pantaloon duck, white gooseneck quacked: Webcor, Webcor