Ed Gallagher wrote in the comments:
A difficulty with your take on the rabbinic discussion of what "defiles the hands" is that the rabbis not only discuss writing material and styles, but also specific books. For instance, Ecclesiastes or Song of Songs (m. Yad 3.5). This seems to mean that certain books would not defile the hands under any conditions, while other books would defile the hands if they are written in a certain way. So the issue is one of sanctity (= defiling the hands), which can only occur if certain conditions are met. The book itself has to be holy (= canonical), and it has to be written in a certain way and on certain material. You are right to point out that more than just canonicity is involved, but I think that canonicity (= status as scripture) is one of the things involved.
First, let me challenge your definition of canonicity. I do not believe that we can equate "status as scripture", a religious and theological category with "canonical status" a literary category. The two may certainly overlap, especially in Judaism and Christianity, but both also developed canonical works and lists that are "scriptural", for example, and certainly the Greco-Roman world around them had canonical texts that were not scriptural, if they even understood what "scriptural" might be.
Second, you report the typical interpretation of the phrase. The problem as I see it is that it lacks evidence, and of course is contradicted by other dicta in the Mishnah's corpus. There is no evidence that the rabbis had in mind ALL copies of Ecclesiastes say and all translations in their pronouncement, and of course had no way to enforce it even if they did so mean it. Further, they don't bother to list for us all the books that "defile the hands." There is also that lovely debate between the Pharisees and Sadducees regarding the books of Homer, which according to the Pharisees the Saducees believe make the hands unclean. Are we seriously to believe that the keepers of the Temple and the High Priest's party placed Homer on a par with Moses, David, and the Prophets? Or reduce the comment to mere insult hurling, and the rabbis simply don't record the Saduceean response? The last speaker in rabbinic lit usually is the winner.
So here it is in a nutshell for me:
1) there is no evidence directly connecting the idea of sanctity to canonicity: i. e. that sanctity is the cause for a text to be considered canonical
2) There seems in some groups any way to be a way in which a holy text is not necessarily canonical: how else do we explain the reference to Homer and the Sadducees without a reduction to absurdity?
I rather think the direction flows the other way: the book was canonical, copies of it were in the Temple, it therefore must be determined if the object is holy or not. Thus, the canonical status comes first, the sanctity second rather than the majority of thinkers who have it the other way round.
I realize that this isn't an adequate response, especially for a view that goes against the usual interpretation and understanding. But it will have to do for now.