If it were me, I'd try to narrow down the source of the issue to either a hardware or a software problem.
Close any instances of the Channels app you have running in your house. Since you have a two-tuner HDHR device, launch two instances of the HDHR app (can be on the same PC, or on separate devices in your home), each on a different channel. Browse to the IP address of your HDHR device so that you can look at which channel is on which HDHR tuner. Kill the instance of the HDHR app that's using the tuner you want the Channels app to use. Now, launch the Channels app and it will use this tuner since the other tuner is still being used by the remaining HDHR app.
The HDHR app doesn't share tuners, so another test you can run would be to launch two instances of the HDHR app tuned to the same problem channel and then use the web interface to your HDHR device see if there's a difference between the signal integrity between the two tuners (or just watch the video on both and see if there's artifacts in one and not the other). If you see visual discrepancies between these two app instances, that would point toward a hardware issue in your HDHR device and there's little that the Channels app can do to mitigate that. GIGO. Now that I think about it, I'd do this test first.
If you do manage to determine that it's a hardware problem, you might want to post details on Reddit (r/hdhomerun). Silicon Dust has support people that watch that forum and have worked with users in the past that have hardware tuner problems and were looking for ways to disable a suspect tuner.