I got this working by switching to Vimeo Pro to host the videos. But, I want to sum up what I experienced, so there is a record of it.
I placed the .json file, the thumbnail images, and the short-form videos for the channel in a subfolder of one of my company's websites, just to perform a "proof of concept" for the channel. While creating the channel, I tried to point to the .json file in the subfolder I created. When I did this, I received an error stating:
"The server returned an unsupported content type. Was expecting 'application/rss+xml', 'text/xml', 'application/xml' or 'application/json' but received 'text/html'".
So, after some trial and error, we moved to an online json store to host the json we needed, and that got us past that issue. But, when we tried to point to the videos hosted on our network, we still received errors. Everything in the channel looked OK in the Roku web interface but, when I put the channel on my Roku and tried to view the videos, it would try to load the video, then it would stop and return to the main page of the channel without ever showing the video. To get around this, I created a Vimeo Pro account, uploaded a video and, after some trial and error with the video URL, I was able to get the channel to work.
I believe one part of the problem is that IIS is not returning the correct content-type for the json and for the videos (the thumbnail images load without any problem). I tried to get this resolved with our admin folks but, since this is just a proof-of-concept, there wasn't a lot of will to track down the issue. So, I just worked around it. There may also be an issue with the video format that I am using. Vimeo did a format conversion when I uploaded the video, so that may have solved the format issue.
I still have questions, and I still can't say I know how to host my own videos for a Roku channel but, the proof-of-concept is working, and I can move on to the next thing.
Thanks very much for your help.