A solution to this problem has already been introduced. Tiles outside of your cities' BFC still influence stability, but they have their own threshold. Their effect shows up as "Outer Territory" or something like that in the expansion tab of the stability advisor.
This seems like a perfectly good solution to me - in almost all my games, even when I have huge amounts of culture outside the BFC, "Outer Territory" only ever reaches about -10, whereas "City Territory", which I assume means BFC, can easily reach -60.
On another stability subject, what's the influence of religions on stability when running secularism? It seems to be -1 stability for every religion in every city, which seems a bit excessive. I had -57 stability from religions throughout my Prussia game after running secularism from the start.
Is there any way to counter this, other than switching back to a religious civic and running Persecutions?