I'm sure this is technically true, but I actually don't think this has much bearing on our discussion. Changes in temperature do indeed increase the ullage, but I suspect this is due to bulk transport rather than diffusion, and bulk transport largely requires the pressure differential. Diffusion will simply flow in the direction of the gradient in the partial pressures, which for a constant temperature is proportional to the relative humidity on each side of the cork (which seems reasonable to assume that any temperature changes under most cellaring conditions will also have a small enough gradient in both time and space that the temperature in the bottle and outside it can be assumed to be the same). Now, since there are many bottles that are hundreds of years old and haven't lost all their contents, it would seem that the diffusion rate must be tiny. It's almost certainly real and measurable, but on the timescales we're interested in, I don't think it will make any difference.
Again, the humidity in the bottle is 100%. Another way of thinking about what 100% humidity means is that the rate at which water molecules are leaving the surfaces is equal to the rate at which they are condensing back upon them (to a good approximation, but surface interactions exist). Once the cork is wet it cannot dry out in these conditions, save for loss to the external environment, which is definitely very low, which we again know thanks to the existence of old-ass wine bottles. There may be some capillary action effects, but once these channels are wet they're not getting any dryer if the bottle is stood up. I suspect much of the loss that's attributed to dryness instead comes about from the cork simply ageing and falling apart, irrespective of the conditions in the bottle, allowing for quicker diffusion or even bulk transport through the neck of the bottle.
Stacking bottles on their sides is almost always the most space-efficient way to stack them. I think most of the lore that surrounds doing so now came about because everyone already did it and people assumed there needed to be another reason for doing so.
All that said, since we know stacking them on their sides works well for ageing and is an efficient use of space, I see no reason not to stack them on their sides in the absence of hard evidence that there is a better way. I'm just very skeptical of the traditional reasons people list for that method of stacking.