As for reliability with blackmagic inputs, they are super reliable but Isadora is still using very old technology to capture. If you use them with current technology (actually it is now a few years old so we are a little behind in izzy- unfortunately it also contains the GPU decompression that would make these kinds of capture units useable)  ie. AVFoundation capture they are perfectly reliable (actually I have no trouble with them in Izzy either - there is just a hitch that in SD they default to NTSC but Izzys setting save function can get by this). In general however I see much better performance with AVfoundation based capture (keep up to date drivers?? I am unsure what problems you guys experience with the BM gear - mark recently updated to a less archaic capture method to allow for the new retina webcams this would MAY have given you an input ordering change, as do some of the updates to BM drivers - very few of them and different hardware models also changes the input numbering but without changing the drivers or capture libraries it is rock solid- I hard coded it into quite a few apps and they run every time). As for the video card settings, BM takes broadcast video standards but admittedly they do not have a good EDID control stack on their HDMI inputs, having said that across a large number of  macs and PCs I have never had any trouble feeding BM gear as long as you know what you should be sending to it and send the right thing- just basic settings.

At any rate it would be good to test this device- I would guess as it is quite new it is also created to make use of current technology to decode its compressed stream (not the outdated quicktime or QTkit frameworks we get in Izzy). Does not look so hopeful for Izzy right now though.