Captain reported severe turbulence encounter with loss of control; resulted in altitude deviation and ATC failure to understand crew recovery request.

Narrative

Declared severe turbulence and requested lower altitude to recover airspeed. Once airspeed was recovered requested higher altitude and ATC seemed irritated at the request due to not having reached requested lower altitude. We weren't climbing back up. We had not descended to anticipated recovery altitude. AP disconnect due to roll authority flag. Climbing out slow due to turbulence and subsequent upset reduced airspeed to point of shaker for a brief moment. Upset recovery initiated with a turn away from weather north of track and lower altitude requested. Descending through FL3131 XX_20. Requested higher and got reprimanded for my requests as if the procedure was optional. We were climbing at turbulent airspeed and all passengers and flight attendants were seated per predeparture request. No injuries reported and flight attendants check in resulted in expected result as such. Instruments were difficult to interpret for a few seconds which resulted in a slow recovery due to inability to focus visually. We lost around 50 knots of airspeed and briefly received a stick shaker. I don't believe speed was the actual reason for the shaker as much as the wind shear itself. The airplane responded accordingly to inputs after auto flight disconnect occurred.