I have been playing with an apple tv 4k running the cox contour app with an hdmi capture device the past several weeks. The contour app has been so unreliable with video freezes and or audio drop outs that Ive abandoned that approach of using it as a tuner for channels, and am now using individual TVE channel apps like the NBC app, syfy app, etc.
If you do decide to use the countour app, I would first test it as a stand alone service to see if you also observe the same video freezes before trying to use an hdmi capture device. Its infrequent enough to drive you nuts when trying to use channels to record or time shift something. It can go several hours without an issue, but then the video locks up in the app while audio continues.
I took the hdmi encoder completely out of the equation and observed the app itself hanging.
It took a lot of debug time and troubleshooting before I was able to narrow it down to the app itself.
Also if you google ”cox contour video freezes” , you will also find lots of complaints from cox customers using the contour box itself with similar issues.
So far the discrete TVE apps are looking much more reliable for me with no freezes.
Your milage may vary, but just wanted to potentially save you a lot of headaches before you decide to put something together.
Im not saying that you will get the same freezes that I observed - but it may be a good idea to run the app or contour box for a week or so and if you dont observe any freezes then move on to the next steps if you decide to go that route.