Funny you should say that - I've just bought an ATEM Mini Pro, and it can capture direct to USB which is quite handy. I'd need to look as to whether it applies any kind of processing but it might even be interesting to test if it can be used to negate the dithering by acting as an active HDMI processor between the computer and the monitor.
If you're able to provide your software I'd really appreciate it and could continue to post dithering tests of different cards as and when I get my hands on them. I'd be tempted even to order cards from Amazon, test them and return them and post the results to try to find a 'safe' list.