What is the more widely endorsed view of longtermists?
I largely agree with your “distant countries” objection. Just because something is practically implausible does not make it morally wrong, or not worthy of attention. I also think it’s not necessarily true that implementing longtermism requires radical changes to human psychology or social institutions. We need not necessarily convince every human on the planet to care about the lives of future generations, only those who might have a meaningful impact (which could be a small number).
Nevertheless, I think the other three objections that you don’t mention provide some interesting and potentially serious challenges for longtermism, perhaps for weaker forms as well.
Perhaps that could have been worded better in my summary. It is not that we cannot predict what could boost medical research in the far future. Rather it is that we cannot predict the effect that medical research will have on the far future. For example the magnitude of the effect may be so incredibly large that it might out prioritize traditional existential risks, either because it leads to a good future, or perhaps to a bad future. Or perhaps further investments in medical research will not lead to any significant gains in the things we care about. Either way we don’t have a means of predicting how our current actions will influence the far future.
With regards to value, being alive, having the ability to do what we want, and minimizing suffering, might very well be things that people in the far future value, but they are also things that we currently value now. On the authors account therefore, these values can guide our moral decision making by virtue of being things we value now and into the near future and referencing that they will also be valued by the far future is an irrelevant extra piece of information, i.e it does no additional work in guiding our moral decision making.