I do not have the time to fully respond to or thank you enough for this essay Steve. This is a much, much better summation of pretty much everything I think about Positivism, Popper, the analytic foundations of CS. There are sections that made me laugh out loud from recognition.
So, it seems we have a profound tension in CS, as in philosophy itself. The quasi-Aristotelian influence of Alexander and the GOF, which emphasizes wholes, patterns (forms?), and the Positivist influence which emphasizes mathematical correctness, algorithms, reduction of problems to their smallest components. There are clearly problems with both approaches, which is why both philosophically and with regards to coding I've gravitated towards the process-oriented philosophers: Bergson, Whitehead, Husserl. (Husserl not really a process guy, but he has much to say here and has much in common with Bergson.)
I'd say the great 19th Century thinkers, Kierkegaard, Dostoevsky and Nietzsche all have indirect implications here as well, but it's a lot harder to map onto CS concerns -- but I think it can be done.