Like I stated, this won't do it. Border not bright enough? Camera can't see it. Border not thick enough? Camera can't see it. So, if it has challenges just with that, it's more than a stretch to think that the camera would be able to accurately discern a black screen from a dark colored plastic frame in order to get any sort of decent reference for extrapolation.
With data processing "garbage in" always means "garbage out". That white frame is the best reference you can get. The only way to get rid of it is to find a way for the camera to see it, or an equally good alternative to it, and not the player. Hiding things on-screen is exactly the challenge which faced 3D displays. That's why viewers need to wear active shutter glasses and anyone not wearing them sees a mess on the screen.
There's only one way I can think that something like this might work, and that would be against a bare wall with IR strips back-lighting it. Then, with the aid of a second camera with an IR-pass filter and during the calibration, the software figures out the difference to provide the offset to the screen.
But honestly, if you are going to do that, you might as well just use IR beacons and draw virtual lines between them for the reference. As cheap as LED strips are nowadays, and the fact that they can be had in IR as well as pretty colors, it puzzles me as to why anyone serious about these setups isn't just using those for reference points. If done right, there are even ways for these to provide more information than just screen delineation.