After more playing, I've found you really don't want to combine the bridged-T within the James circuit. It is much better to keep them on their own.
If you think about it, the two circuit fight each other, if you roll them together. The james is trying to control bass and treble, while having indirect control of the mid. The T-filter fights that, because it's trying to form its own mid-dip, and probably not at the center value the James circuit is using.
Another way to look at it, from a tech point of view, is that by inserting the T-filter, you just screwed up all the RC values set within the James which makes it work as intended. The James circuitry is also screwing up the RC values of the Bridged-T that allow it to work as intended.
So the answer is to keep them separate.
And so you know, this has mucked the process of my current build, in a good way. The amp I'm building has a T-filter in it, apart from the regular Treble/Bass tone circuit. I thought I knew how some versions of this amp incorporated a "Contour" control. Turns out I was way wrong, because the Contour alters values in the T-filter, and I wasn't using that approach.
In the end, I'm fixing the implementation of the Contour control in my build, plus adding your idea for mid control, for a much more flexible control of midrange.