I have a feeling of deja vu that I'm going into the world of Mcrit and beyond again. The constant AoA theory would work just fine for an aircraft that did not operate in the transonic region, i.e. below Mcrit. For an aircraft operating in cruise above Mcrit (and that's just about all jet aircraft at NORMAL operating levels), AoA alone is not enough to consider.
This one requires a picture, a picture is worth a thousand words. Stand by for said picture/s with associated text within a day or so. (I need to 'borrow' my son's web site to post the pictures, and he's aviating just now).
Regards,
Old Smokey