But you are receiving a SD feed not HD.
But if you get the 7D and you don’t hit record, push that white box all the way up and record to your device. Then in post zoom in just a bit to crop out the box. If you hit record in 12 minutes you will get the stop recording message in your video.
You will need a HDMI splitter and an external monitor.
So I think you have a chance to pull off what you need with a little extra work in post. You can do the cropping in Compressor the same time you convert to ProRes if you like.
BTW, love the Russian Ark, Wish they would overdub it in english so you could just watch the video without having to read the subtitles.