I’ve just noticed that Caleb of DSLR Video Shooter has built and integrated case, with monitor, for an ATEM Mini Pro. It includes on/off switches, headphone out, hdmi-out routing for external monitor and cheese plate mounting for attachment to rigs. It seems fairly comprehensive and includes some passive cooling options which might be its weakest point.
He’s put a video on YouTube and also has detailed instructions on his blog for the construction. It seems pretty comprehensive but he’s also seeking feedback in the comments on YouTube … just the sort of thing that folks on here are probably going to be good at. Total construction price (inc monitor) was approx $375 iirc.