Worldbuilding and Single Sunrises

OK. This thing has been bugging me on and off for about two weeks now.

No matter how incredible the "what if there was a world that only had one sunrise [for hundreds of generations]" idea is...I can't think of a way to make it plausible. Or, even if you could, you certainly couldn't have people "lined up on the eastern horizon" to watch it.

I'm not a science or math kind of person, so maybe I'm dead wrong about all this. And if you can think of a way to make it work, I'd really love to know. I've just kept coming up with dead ends.

Por ejemplo...

• Assuming that the inhabitants of this world are natives to that world, they'll have lived hundreds/thousands of years in darkness. Their eyes and such will be adapted to/created for that kind of world. They won't be able to handle the piercing brightness of a sunrise.
  
• And what would happen to the plant life of the planet? You'd end up with something of a wasteland, I'd think, when the sun came around.
  
• Exactly how slowly would this planet have to rotate? Can planets rotate that slowly?
  
• What sort of whacked out weather and temperature conditions would this planet have? And what sort of atmosphere would be necessary to prevent super-extreme hot and super-extreme cold?

I'll give Dr. Root credit for a wondrously glorious and inspiring image. But I can't make the stupid thing work!

Would transplanted humans solve some of the problems? What if the sun came around at regular intervals (albeit super-longly-spaced ones)? Could everything be like the 13-year cicadas? It would have to be more like 1300 years, but it might be a possibility. What if this hypothetical world were flat? The scenario would actually make a bit more sense. Sort of.

The best solution I can think of is to roll with the absurdities of the matter, and push the thing REALLY far into the realm of fantasy. The earth is flat. The sun circles it. People survive. Plants survive. Why? Who cares? It's the way this place works. Our natural laws don't apply in these cases. Deal.

Lewis wrote Narnia as a flat world. So it's not impossible to pull of. And Lim has some even crazier worldbuilding going on here. And Martin has his non-sensical 30-100 year seasons. Maybe there's a bit of hope for it. :)