Just set it up as you suggested. Ill give it a few days, but I don't have much hope for it. I think I'll have to end up replacing the screen, which is a bummer. Seems like you should get at least a year out of a CPU block without having to replace a major component.
While I agree in principle, I expect the screens themselves were not designed for single image display. You see this a lot on OLED televisions in shops, where the static adverts start to burn in.
I also know that even my phone OLED would suffer at least long-term image retention, if not permanent burn-in, if I only ever displayed the one static image. As is, I get it slightly after just a few hours of using the Kindle app and it takes a few minutes before that starts to fade away. I can only presume it's a limitation of the screen technology, rather than anything specific to AC.
I'll be buying one myself soon anyway, so we'll see....