if we make a simple replicator and have it successfully reach another solar system (with possibly habitable planets) then that would seem to demonstrate that the filter is behind us.

Excellent! So, wouldn't that mean that the best way to eliminate x-risk would be to do exactly that?

It is counterintuitive, because "eliminating x-risk" implies some activity, some fixing of something. But we eliminated the risk of devastating asteroid impact not by nuking any dangerous ones, but by mapping all of them and concluding the risk didn't exist. As it happens, that was also much cheaper than any asteroid deflection could have been.

If sending out an interstellar replicator was proof we're further ahead (i.e. less vulnerable) than anything that could have evolved inside this galaxy since the dawn of time, it seems mightily important to become more certain we can do that (without AI). If some variant of our interstellar replicator was capable of enabling intergalactic travel, that'd raise our expectation of comparative invulnerability because we'd know we've gone past obstacles that nothing inside some fraction of our light cone even outside our galaxy has been able to master.

Ideally we'd actually demonstrate that of course, but for the purpose of eliminating (perceived) x-risk, a highly evolved and believable model of how it could be done should go much of the way.

Of course we might find out that self-replicating spacecraft are a lot harder than they look, but that too would be information that is valuable for the long-term survival of our species.

Armstrong and Sandberg claim the feasibility of self-replicating spacecraft has been a settled matter since the Freitag design in 1980. But that paper, while impressively detailed and a great read, glosses over the exact computing abilities such a system would need, does not mention hardening against interstellar radiation, and probably has a bunch of other problems that I'm not qualified to discover. I haven't looked at all the papers that cite it (yet), but the once I've seen seem to agree self-replicating spacecraft are plausible.

I posit that greater certainty on that point would be of outsized value to our species. So why aren't we researching it? Am I overlooking something?