Try the A/C System Self Diagnosis. It's easy and quick. This essentially tests your A/C sensors and the CAN system: Start vehicle. Turn off radio. Hold the "Setting" button while twisting the "Volume" knob back and forth until the Self Diagnosis screen shows up. Scroll down to "Confirmation/Adjustment" and press "Enter". Scroll down to "Climate Control" and press "Enter". Wait for fault codes to display in the ambient temp display area. The test shouldn't take long. Graphics stop moving when the test is complete. There are some other tests in that menu, like a button test. Feel free to play with other tests. To exit, press "Back" repeatedly until you back out of the diagnostic mode. The A/C-A/V system will then reboot.
Post your two-digit numeric fault code here, if you get one. A zero ambient temperature reading is a good test.
If zero, then it's probably an Air Mix Door problem (assuming the entire coolant system is working as advertised). Without tearing apart the dash yet, try cycling through all 5 modes for the ventilation doors, but always feel the air temp at the foot air vent, since there is always some air coming out of that in all 5 modes, and it's more likely to be warm than the upper vents. If you never feel warmth, it's probably the air mix door, which allows conditioned air to flow through the heater core. If no warmth, switch to full defrost mode and try feeling for warmth by the windshield defrost vents; if air is blowing but not warm, that can probably confirm the air mix door problem. The Air Mix Door is the only door that can completely eliminate heated air from flowing through all vents. Oh, as an afterthought, make sure you vehicle is completely warmed up for any of this venting business, otherwise, you'll never feel heat. There is no auxiliary electrical or gas heat option in this vehicle as there are in other vehicles from the North (Volvo, Saab (pre-GM), Winterfell, et. al.).
The first door on the other side of the heater core is the MAX-COOL door, which doesn't have much mention in the maintenance manuals, but doesn't completely close off heated air. It's less of a door, per se, than a constrictor of airflow allowing air to most always get around it no matter its position. It's off-state is in an intermediary position (like an airfoil), along with bilevel, foot, and defrost/foot mode. It only moves for upper vent and full defrost modes. In full defrost mode, it shuts off conditioned heated air to upper vents and nearly all (90%) air to foot vents. In upper vent mode, it turns the other way, which creates a straight path for conditioned cool air to go to the upper vents, with very little (5%) for the foot vents (in combination with the Ventilator Door). I wonder if this door could get out of sync with the Ventilator Door, with which it seems to interface. This MAX-COOL door could be your problem, based on how you describe your system's function, but I'm not sure it would decrease airflow as much as you describe. Maybe.
The last door after the heater core is the Ventilator Door, which only controls the conditioned air going to the upper vents or foot vents. This little guy would be very obvious if it was not working. It does interface with the MAX-COOL door, so if out of sync somehow, it could be stuck in an intermediate position.
The Defroster Door is another door in the system. It opens only for foot mode (but not always), foot/defrost mode and full defrost mode. In combination with the other doors, it allows 0% - 30% of air while in foot mode, 40% in foot/defrost mode, and 90% in full defrost mode. I don't think you have a problem with this door.
Additional shower thoughts:
There is a way to check all of this electrically, but you start by pulling apart the dash then testing leads on connectors. Pulling apart a dash is what we try to avoid, right? You may need to do just that to avoid shotgunning parts. It would appear that door motors go for $12-$50 where you get all the parts your car will ever need. I'm wondering if your heater core is obstructed with something other than an Air Mix Door? I'm not sure that is possible; it's deep in the system. Well, that just makes it possible then, doesn't it. Especially, if air flow decreases when you are demanding heat. Unless you find a ventilation mode for a work-around it would appear you'll be diving into a dashboard. Condolences. Just for giggles, before diving into a dash, check the temps on your heater core hoses (but, I don't think your problem description merits this): Use your hand to feel heat in both hoses along their entire length, or use that laser temp gauge gun you probably gave your significant other last Christmas so they could measure the oil temperature in your deep fryer. It drives cats and cat-like dogs to frenzy, too. The engine needs to be fully warmed up for this, too, with heat commanded on, so this test won't be comfortable if using your hand.