So now I've printed the 90mm, though I've kept the Thumb 2mm from the edge of a 75mm square:

This is in the event that I use the 4.12" screen. I wanted to see what kind of bezel would be apparent.

It seems that a 90mm square is large enough for my hands, so the next step was to see if there was any display that was that size. The good news is that there's a single panel that is the size: S050QWS115EN

It seems that, when the cable is folded, this screen would be max 4.4mm. It also seems that it's straightforward to connect to a PCB as the pinout has a single power pin, MIPI related pins, 2 backlight pins, a reset pin, some "LCM_ID" pin and the rest are either GND or NC.

The slight issue is that this screen is shockingly recent -- the datasheet was finalised on the 14th of June this year. The price is also "Enquire Now", though at least the MOQ is only 2pcs. I've sent a message to Dwin, the guys that seem to take screens like this and turn them into HMI's, to see if they're developing anything (because if they are, I can focus on the solar cell in the meantime).

The backlight takes 18V and uses up to 2.3W, but the good news is that the screen acheives a minimum of 900nits, meaning that it's viewable outside. If I ever use this panel, I'd have to make sure to have something like a high frequency backlight circuit so that low luminosities dont flicker.