It makes perfect sense... But the OP to say "But I felt a significantly more difficult inhalation the moment I turned myself facing to the surface "
Talking rough numbers, lets say the lung center-mass is 12" from the center of the regulator diaphragm when the body is vertical in the water column and facing forward. The actual center of force on the lung may actually be lower on some people since the rib cage deflects a lot of hydrostatic force (pure speculation on my part)? Looking up moves the center of the regulator diaphragm about 6" higher in the water column. I can see a rapid 50% increase in water pressure being noticeable perhaps moving over the threshold where this individual can sense it or not.
Unless I completely misunderstand the question, it is more an issue of activation pressure on the second stage than the flow rate. I know that I have to be very relaxed in dead-calm warm water without a suit and concentrate to detect positional difference. I doubt that changing the second stage would change that. Even if the second stage was badly tuned, it would be equally poorly tuned in any position.
If I remember correctly, the Conhself 14 (hate Roman numerals) is an unbalanced second stage with a larger diameter diaphragm. This would theoretically work against you requiring more lung force to activate against the differential pressure on the larger diaphragm surface area.
The unbalanced part isnt the issue other than it requires a larger diaphragm to activate the demand valve. Both the Conshelf and Atomic regulators produce about the same performance in instrumented breathing machines. The big variable is individual bio-mechanics. Maybe your body structure around the lungs is more effective at deflecting hydrostatic pressure than mine or the OPs? We know the physics is sound; it is only an issue of being able to sense it.