What about adding one of those inexpensive USB capture cards to the USB port on one or both of your single-port LinkPi Encoders? I know several people have done that with good results, and I believe the devices are less than $10 each.
Here's one that's reported to work: Amazon.com: Audio Express AXHDCAP 4K HDMI Video Capture Card, Cam Link Card Game Audio Capture Adapter HDMI to USB 2.0 Record Capture Device for Streaming, Live Broadcasting, Video Conference, Teaching, Gaming : Electronics
And, a post referencing it:
