OK, my prior statements said 'maybe' some clockwise rotation and pointed out you had CCW inclination already. Your CONSULT with the maxfax cross referenced that 'maybe' and resolved to getting CCW as part of the correction and I confirmed that made sense to me.
Now the 11 degree angle I marked out is one where the GREEN line is an absolute horizont where the BLUE line is a basic line from anterior to posterior nasal spine (ANS-PNS)--maxillary--showing you have CCW orientation already. So, if the blue line is rotated in a ccw direction, there would be more CCW orientation than you already have and since the green line is a constant relative horizont, the angle would INCREASE with more CCW.
So, your docs findings (at least to me), convey that more CCW than you already have is needed to open the bite so the deep bite is not 'IN THE WAY' of advancing the mandible. So, that RULES OUT the 'maybe' clockwise. So, he's saying he's got to angle UP the ANS-PNS MORE to get the DEPTH of teeth overlap OUT OF THE WAY in order to advance the mandible. If not, the mandible can't be advanced as the deep bite makes too much of an overlap that gets in the way of lower jaw advancement.
Hence, based on your doc's findings that basically tells us he HAS to rotate CCW to OPEN the deep bite INORDER TO move the mandible forward, we have to RULE out the 'maybe' of clockwise rotation.
Although the CCW rotation (along with braces to angle out the front teeth) will help close in on the overly obtuse nasial labial angle, the nose also can rotate upward with that. But still, there would be a net decrease in the NLA.
[I remember, over 11 years ago, when I first consulted with a maxfax about getting my jaw advanced where at the time, I didn't know I had a deep bite, he asked me what did I like best about my face and I told him' 'my NOSE'. He told me the rotation he would have to do to advance out my lower jaw would be rotating my nose upward and it seemed at the time, his implicit assumption was that I would NOT like that look because my nose was great which is probably why he asked me what I liked best about my face. That said, I KEPT my maxfax deformity because I did not want to alter my nose.]
I tend to think that Class 2 division 2 which is the deep bite with the retroclined front insisors along with recessive mandible is the most problematic to fix. Consider that to make it look better in the MIRROR one has to lower their jaw in order to advance it out so the upper teeth meet the lower teeth where when doing that, you find that the back teeth are not meeting and there is a big GAP between them and what one is doing is in direction of clockwise rotation of lower jaw. But IF the surgery just advanced out the lower jaw with clockwise rotation of the lower jaw, (as done in the mirror to make face look better) then you would have posterior open bite.
I understand your DILEMMA simply because the DEEP BITE if one had a big extent of it, IS a dilemma where the dilemma arises from their needing to open the bite via CCW in order TO advance the jaw forward, even IF you already have CCW orientation where doing that is not going to give the clockwise rotation to the jaw which one usually does in mirror to make face look better when one has the deep bite with recessive jaw. So, it's a DILEMMA where you might not get what you want out of the surgery.