As for the Quality Without a Name, it is here where the rubber really hits the road. How to tackle it? How to give it a better philosophical grounding? I think the aesthetic angle that Alexander chose to describe it was great and part of his genius. It attracted and still attracts a certain kind of person, similar to what attracts people to books like the Zen of Motorcycle Maintenance, or any Zen of ... book--as evidenced by the multiple references to such books in the linked wiki page.
I'm not sure, however, if this is the right way to present or approach a "metaphysics of software design." Without going into too much detail, I think it would be better to connect Alexander's notion of the QWAN to the Platonic and Neoplatonic "One." There the three transcendentals of goodness, beauty, and truth were contrasted against each other to see how they were different shades (or emanations) of the that one singular thing or quality. Doing so, might give us a way to apply Alexander's ideas more broadly than his aesthetic approach.
The Zen description of QWAN is more about 'what is Quality' or 'where does quality come from'. Yes, elegance plays a part in the overall structure but without QWAN it would be a pretty average 'object'. For example, the design of the car has an 'elegance' in its design but without the Zen 'Quality' would probably not be put together well and be unreliable and shoddy/buggy but it's still a car built with all the patterns.
Quality comes from the knowledge, experience, effort and undivided attention put in by the craftsperson creating the 'object' at a given point in time. The train analogy from Zen explains this well and it's basically about focus in the moment you are doing something. This produces Quality, nothing else. You could argue that the parts to make up the car example above would give it Quality and fix most of the issues in the final product. This is true but only if every step in it's production, from mining the minerals, design, drafting and manufacture were given with the same focus.
As far as software patterns are concerned I think we have strayed too far from inherent Elegance to strive for some other abstracted Elegance (inherent Elegance takes longer to control/master!). The computer is very simple at its low level core (how it computes at least) but we keep building languages to make it simpler at a much higher level and in the process have made things very In-Elegant in between these levels. We had (and still have) languages that take on the lowest level and abstract it to a higher level very simply, the most obvious being Lisp and Forth but the lack of processing power made them untenable for their time. Both of these languages have the 'Elegance' CA discusses, you have complete freedom in creating the language/s and language features you need, put some Pattern Mining in with some Quality and you really have something!