How does the air-circulation in the lower stratosphere look like?
This presentation mentions "Atmospheric Motion Vectors (AMVs)", and specifically mentions a number of AMVs, which separately cover the globe (GOES AMVs ±60N, plus polar AMVs from MODIS/AVHRR/VIIRS, and a combined product from UW CIMSS) but says that are all only 3 layers. That presentation is talking about producing a more global, higher resolution product, but it's only a year old, so I'd guess the data isn't available yet.

However, the UW CIMSS AMV page says that their datasets have 13 layers, so maybe it is suited for what you need. The data is gap-filled with modelled data.