However, what I'm trying to say is, regardless of how the statutes have been implemented, the theory is sound and rational: a patent has multiple, largely orthogonal, dimensions and it should be judged along those lines. To my engineering mind, anything that conflates those dimensions is an inelegant and problematic ruling.

Yeah, the problem with that idea is that rulings aren't intended to implement abstract theories independent of the controlling enactments (the statutes and the Constitution). The theory that patents have "multiple, largely orthogonal dimensions", at least as you seem to identify those dimensions -- and particularly the idea that newness is a consideration only for Section 102 patentability, and not Section 101 patent eligibility -- is inconsistent with the actual text of Section 101, which explicitly requires for eligibility that the thing sought to be protected is (a) an invention that is (b) new and (c) useful.

Your aesthetic preference for orthogonal considerations where newness would be a considered only for Section 102 patentability is, of course, a legitimate aesthetic preference -- but its not what the statute says, and I think it would a more "problematic ruling" for the court to ignore the statute simply out of aesthetic preference for orthogonal categories with a certain configuration.