One I cut for length but keep coming back to.... check whether the room device and the display are on the same power circuit as anything with a compressor. Mini-split, fridge, vending machine. Sags when the compressor kicks in can reboot a PoE injector or knock a display's HDMI handshake. It presents as an intermittent problem with no network signature at all, which means you can run all seven tests above and find nothing. Cheap fix, cheap to check.
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If anyone runs this sequence on a room and gets a result that doesn't fit the table, drop the numbers here. Especially interested in SD-WAN and SASE environments, since media bypass configuration seems to be where most of the surprises live and I'd like a bigger sample than my own.