This daily devotion might save us flights of fancy that are destined, in my view, to end in skepticism. It is here that I fear that exegetes are trying to know the unknowable. I do not see any historical proof that one and only one community either created, gathered, or carried the Q tradition through early Christianity until it wound up in the Gospels of Matthew and Luke. On the contrary, the very fact that Q apparently existed and functioned for some time in each of these evangelists' churches before it was absorbed into their Gospels tells against this idea of one Q community. In sum, I'd simply be careful in claims about Q's extent,community, etc.
Heavy speculation begets a heavy margin of error.