I assume there is a front-loaded initial startup cost of oxygen to initiate combustion that is difficult to do at higher altitudes primarily because the turbine

I assume there is a front-loaded initial startup cost of oxygen to initiate combustion that is difficult to do at higher altitudes primarily because the turbines are not spinning (and therefore aren't pulling oxygen into the engines). Air speed might make it easier to get the turbines up to speed again, but I would make an uneducated guess that the oxygen concentration of the surrounding atmosphere is more important; I think it's likely the engines will contribute much more to turbine rotation than air speed. Moreover, the engines won't come up to full power instantly; they will need time to throttle up as well... in this case, glide time is more important than air speed. Ergo, the altitude is more important for the purposes of restarting the engines. (... Except for the "tangential" need that the operator needs to be conscious to restart the engines, and thus needs sufficient oxygen concentrations in the cabin)