I don't really see how the argument for feasibility of H+ has much to do with the size of the design space for life (and AI, and nanotech,...) as long as its non-empty. After all, there's a huge design space for impossibilities as well. Or am I misunderstanding the argument?

There are some rather mundane improvements (at least compared to the design space) that would be enough (if realized) to show the feasibility -- say, intelligence augmentation, brain-computer hybrids.