By the point of the singularity no human has any instrumental value.
...
humanity will get its shit together and save everyone anyways, because people are intrinsically valuable.

It's a tricky point, I expect humans (in their present form) will also have insignificant terminal value, compared to other things that could be created. The question of whether the contemporary humans will remain in some form depends on how bad it is to discard the old humans, compared to how much value gets lost to inefficiency by keeping (and improving) the old humans. Given how much value could be created de novo, even a slight inefficiency might be more significant than any terminal value the present humanity contributes. (Discarding humans won't be a wrong outcome if it happens, because it will only happen if it turns out to be a better outcome, assuming a FAI.)