The only difference between "explaining the difference between conscious matter and non-conscious matter" and "explaining the difference between living and non-living matter" is that we don't yet know how to do the former.

It's impossible to express a sentence like this after having fully appreciated the nature of the Hard Problem. In fact, whether you're a dualist or a physicalist, I think a good litmus test for whether you've grasped just how hard the Hard Problem is is whether you see how categorically different the vitalism case is from the dualism case. See: Chalmers, Consciousness and its Place in Nature.

Physicalism implies that the "hard problem of consciousness" is solvable; physicalism is true; therefore the hard problem of consciousness has a solution.

Physicalism, plus the unsolvability of the Hard Problem (i.e., the impossibility of successful Type-C Materialism), implies that either Type-B Materialism ('mysterianism') or Type-A Materialism ('eliminativism') is correct. Type-B Materialism despairs of a solution while for some reason keeping the physicalist faith; Type-A Materialism dissolves the problem rather than solving it on its own terms.

Basically, I think that the evidence in favor of physicalism is a lot stronger than the evidence that the hard problem of consciousness isn't solvable

The probability of physicalism would need to approach 1 in order for that to be the case.