If you have the accelerating upwards theory, the air would all have equal 'pressure' put on it. Doesn't this mean it would be the same density all the way through?
No, it wouldn't. Say for instance there is a bottle of some kind of gas. If the bottle is just sitting there, or even moving at a constant velocity, the gas will have equal density and pressure throughout.
When the bottle is accelerated the inertia of the gas pushes against the bottom (or the source-direction of the acceleration, where ever that may be) creating higher density on the bottom and lower density at the top; a density gradient (and thus a pressure gradient, too).