Blackmagic Design Teranex Mini SDI to HDMI 12G Converter is probably not the best choice:
https://www.eizoglobal.com/support/comp ... i_12g.htmllooks like it works only in 4:2:2 mode with Eizo. BM's HDMI implementation is problematic, not only with Eizo but with many different displays including TVs (specially LG).
I would probably go with:
https://www.aja.com/products/hi5-12gbut asked first AJA and Eizo if they can confirm good 444 10bit support.
Aja box gives you very detailed control over output and other parameters.
You have to be sure you will get 444 at 10bit and with Decimator it's not obvious at all. Quite often you get some conversion to 8bit RGB.