If you really want to try this, why not try it first with a small commercial TFT or OLED display? They are very cheap, so you'll be able to mess up a lot. And they don't involve a massive number of pixels, which will be good for debugging.
They also use integrated driver chips which tend to support a handful of different resolutions; I guess that if you cut off the half which did not have any driver circuitry, LED backlights, display bias voltage drivers, etc, you might be able to just tell the controller it has a different-sized screen. E.g., take a 128x64 SSD1306 OLED display and cut it into a 128x32 one.
I don't think it would be very likely to work; there's probably a lot of very fine connections that you might accidentally bodge or short, even with a high-powered laser cut which maybe re-seals the top/bottom layers along the edge. But in that example, if nothing important broke, I think the SSD1306 driver does support a 128x32-pixel resolution and you might be able to just operate it normally.