Fixed it. Appears there were two problems here:
OpenXR runtime was set to WMR. For some reason, because of this, MT Preview always started in the flat screen mode. Runtime can be reset to SteamVR from the SteamVR settings (accessible from the SteamVR status window). I'm actually not 100% sure this step was necessary, because after it, MT Preview still had the same problem it had for me: no picture rendered in the headset.
A second display was connected to a different GPU than my VR was. I'm using an HDMI dummy plug to fake having multiple displays when I'm working in VR. Pulling it out and only having one display connected to the same GPU VR was connected to solved the issue for me. Maybe wrong display and so wrong GPU was assigned to DCS somehow?
