Recovery from the situation you describe would be done by descending down 2000 ft to the next level in order to gain better low speed, high speed, and thrust margins
I may have mis-understood your intent but descending to "the next level" implies adhering to air traffic control flight levels. That is the last thing you should be concerned with during stall recoveries.
Certainly in the B737 Classics at 37,000 ft you can count on deliberately losing at least 3500 feet during the recovery phase to reach a minimum safe airspeed of Vref 40 plus 100 knots as the criteria for levelling out. Add another 2000 ft to reach Severe Turbulence Penetration speed if still encountering severe turbulence.