I see a significant aerodynamic problem not yet mentioned specifically (but KingAir1978 nudges up close against it.)
DRAG in a slip (where the relative wind is hitting the side-area of the fuselage, not just on the nose).
And thus rapidly-decaying airspeed, if one is also trying to hold altitude. Especially so close to the operational limits of the aircraft (A321 ceiling - 39800 feet).
Slips are a really good way of killing off airspeed (and/or altitude) - see, e.g., the final approach of the Gimli Glider.
Might be on the order of losing 15 kts IAS per minute, even at full thrust. Maybe more, if there is pitch added to hold altitude as the airspeed decays. And depending on all-up weight.
Just how long is this slip ("observation window") expected to last?
"Punctuated slipping" might be a solution - slipping for 15 seconds - return to coordinated flight for 60 seconds to regain speed - slip another 15 seconds (rinse and repeat).
Assuming any other problems can be addressed.