I would use three pieces of hardware for this task.
A recording laptop.
A device that allows you to input the HDMI to the recording laptop, aka, a frame grabber.
An HDMI spliter.
A recording laptop
Uncompressed Prores HQ at 10 bit will yield extremely large file sizes. Is there a reason you want prores? 4K 444 10bit uncompressed would be, in my opinion, better captured as an uncompressed AVI "...