This "model" assumes that the probabilities of "fix the rot" and "find new nest" are independent. I'm not entirely sure of the relationship, but I'm very sure they are not independent.
Also, the assumption "we go extinct" is pretty strong, and IMO, unwarranted.
Yes, I am oversimplifying. It is not a model. Even if the two courses of action are not independent it is highly unlikely that success in one requires not investing in the other.
The premise of the argument that we must focus on the earth instead of space exploration is fundamentally flawed because it assumes that the two are mutually exclusive.
Resources for doing anything are limited (by will, as well as for other reasons). It necessarily follows that putting resources into space exploration reduces those available for "fixing the rot" (although sure, not necessarily by equal amounts).
If fixing the rot were genuinely an extinction-level imperative, I'd say we should devote zero resources to space exploration. However, I don't think there's an extinction-level event or period coming at any point in the foreseeable future, so I don't think we have to be that dogmatic about it. Even so, I'd far rather see us defer all fossil-fueled adventures until (if!) we get this place into better shape.
Also, the assumption "we go extinct" is pretty strong, and IMO, unwarranted.