Okay, so 19x13mm or so. The TinyTV had a pretty bad screen, but the active area you describe. The TinyTV 2 is a little bigger but higher resolution, so if it can fit that's a fairly easy solution. Not much work involved. It doesn't have the greatest off-axis viewing and dark areas glow faintly, like most IPS displays. It does require a press of the power button to power up, though.
I've experimented with the AtomS3 and Lilygo T-QT microcontrollers, which have a pretty small screen. Might be too small for your purposes, though, at 15.2x15.2mm square.
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