And if you wait too long and the screen goes blank, then the Home button no longer lets you switch back to OEM?
Yes, your observation is a huge clue. That narrows down the problematic area quite a bit. The EC unit consists of a video and control switching circuit board, with a smaller attached Android box with the rest of the brains. Your observation tells me that the larger switcher board has no problem per se, and that the problem is either with that smaller Android box (pictured on the right) or the physical connection between the two (e.g. bad solder joints).
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