"Mixed-breed puppy" is, to me, not such a clear case ("breed" is clearly originally a noun, but maybe this use is common enough to have converted). But you don't need to use spurious examples -- in another comment, you provided a very genuine one: "red" and "wooden" are both clearly adjectives, and their ordering cannot vary. This is a well-known example of a somewhat-but-not-entirely mysterious phenomenon in linguistics.
Here's a nice recent writeup of what I think is a related phenomenon: https://stancarey.wordpress.com/2015/04/28/cutthroat-compoun... . This one consists of the observation that words like "kickass" and "pickpocket" are suppressed (not illegal, but suppressed) in English because they conflict with our tendency toward right-headedness (that is, in any English compound, the "essence" of the compound should be found at the right end). Instead, we incline more to compounds like "bank robber" or "nose-thumbing" ("engage in a bit of nose-thumbing"). Someone else in this thread already mentioned that they see adjective ordering as a question of which adjectives are more essential to the whole.
My problem with your comments here is that you're making arguments based on obviously spurious tests unrelated to the claims you then try to follow (um, lead) with. It's analogous to saying "We need to stop celebrating Thanksgiving by eating turkey. Turkey perpetrated the Armenian genocide, genocide is bad and should be stopped, QED". Stick to honest examples, and you'll find the problems you're talking about are rather muted. Don't let your feeling that the problems are large, and you therefore need extremely malformed examples, lead you into choosing examples that are extremely malformed because they exhibit a completely different problem.