There is another service that you can use called PlayOn Desktop and PlayOn Cloud to record shows from on-demand services like Amazon Prime. The PlayOn Desktop is a Windows only application and uses your login credentials to various on-demand video services. It will then stream the video and capture the video to your computer. PlayOn Cloud does the same, but captures the video in their cloud where you can download the MP4 or stream to your device. PlayOn Cloud will delete the cloud file after a couple of days.
These are available at PlayOn.tv. PlayOn works with Amazon Prime, Netflix, Hulu, YouTube, HBO Max, Disney+, and many other Video-on-demand services, you just have to have credentials for the services you want to record from.
With PlayOn Cloud you purchase credits (about $.25 each) and then each recording uses 1 (720P) or 3 (1080P) credits. PlayOn Desktop is currently on sale for $40 for 12 months. PlayOn Desktop used to have a lifetime plan and may offer it from time to time. I added the folder where PlayOn saves videos to to Channels DVR's Local Content and watch the video's using Channels DVR.
Another on-demand recording service is called AnyStream from Redfox.bz. It does record in 1080P 5.1 Dolby Digital, but is currently limited to Amazon Prime, Disney+ and NetFlix.