It is correct that humid air is less dense than dry air; but so is warmer air.

Theory
Warm air rises. Warm air has more moisture holding capacity. Thus RELATIVE humid (remember, temperature dependent) decreases.
The absolute moisture content in the air is probably more consistent, but due to temp differences varies at different levels with the temperature.
This could also be an effect if the floor is cooler, especially if you are sitting on a slab and then slightly cooling the air directly close to it ==> rise in Relative humidity.

I would be curious to see what thermometers read at various levels.

I agree a small recirculating fan would help. It wouldn't take much, nor have to run all of the time.