One more consideration is targeting data. Do you even have another target or the sensors to find one ? The means of detection for a suitable planet or even just a good solar system, where you build a bunch of habitats might require huge telescope arrays or even something like a special telescope that uses the Sun as a gravity lens source.

Might be out of reach for even a massive generation ship.

Then you have a natural upper bound on the amount of amenities etc, because if you provide too much, 1000 generations can probably use it to try and find another target.

I'm sure you can keep making the situation more and more specific, but that's not going to increase your chances, or make the whole thing morally acceptable.