Greg, the later (LUTs loaded from SD card might be doable, but the HDMI connection on the VA is a video input/output on,y, no camera co tool functions, even on BM's Micro Cameras, which many users previously asked for similar capabilities, controlling camera menus, etc.
The Record trigger function on the VA, the VA receives a "record trigger" command from the camera (Record Trigger mode) or reads the Time Code (T/C Teigger mode) being sent from the camera, both of which start the VA to record the incoming video signal. While HDMI can be used for some control functions on a DSLR, this useually is set to allow a TV monitor to start/stop in camera playback when the camera is connected to a TV monitor. SOme newer DSLRs have BlueTooth or WiFi remote support using IOS (Apple) or Droid applications, but this is not done via HDMI.
If you want to start/stop the record on your camera remotely, and record to the VA also, just use the camera remote IR controller, or a cabled remote start/stop controller (electronic version of a cable release). These can be attached to the top of the VA (1/4x20 screw mount or Velcro). Then with "Record Trigger" enabled on the VA, then starting record on the camera remote wil, start both the VA and camera recording.
DS