I have a similar solution in place. For reasons ... I have a machine that is 100% locked down by the client. I cannot install software on it, nor does it have any sort of remote access tools installed on it. To keep my work space clear, and negate the need for second monitor (as I need to be able to see the screen of this machine AND my main machine at the same time), I use an Elgato CamLink HDMI dongle[1] to capture the video output of the machine, and I use VLC to display it in a window on my main desktop. I use a bluetooth keyboard and mouse combo to control it. The latency on the video capture is very low (it doesn't feel any more laggy than a normal remote sesson), and as an added bonus I can screen capture the video stream, which is really useful for documentation. The CamLink is locked at 1080p, so as long as the machines desktop resolution matches that, I get a very crisp picture. I've been using this setup for almost two years now, on a daily basis with no issues.
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