Peter, I was thinking that this inflection point could be handled without having to do a full retraction. You could coordinate motion between the A, Z, and X axes to sort of freeze the endmill in place and successfully rotate the A axis 180°. If you were surfacing something where the angles were less than 90° than this is less of a problem area. I have seen 5 axis heads for waterjets that function as I describe, though they max out at less than 10°.
Routalot, this head from Zimmermann includes a B axis in addition to A and C:
https://www.f-zimmermann.com/en/milling-heads/m3abc/
They seem to have lined up the centers of rotation well, though I agree that it would be a challenge to control something like this.
Muzzer, my intent was to design a milling head that would give the additional 2 degrees of freedom rather than something mounted on a table.
Rob, I can't quite tell from that photo, but are you mounting two routers side by side with each on its own Z axis? I've seen that on production machines but that's not my goal here.
Thank you all for the excellent input.