2006 Odyssey imbalance driver/passenger air temperature imbalance

[oldtechie]

I am asking for opinions on a problem with a 2006 Odyssey EX-L heater/air. The air from the left (driver's) side is consistently colder than the air from the passenger's side. Air flow rate is good on both. This occurs both in summer, when A/C is on, and in winter when only heater is being used. In winter, plenty of hot air is available on passenger side. We have been managing by blocking the driver's vents, but this is a poor solution.

Via video, the dealer confirmed that the doors (dampers?) are working OK. Dealer diagnosed a plugged heater core and wants to replace it: parts and labor ~$1500. This diagnosis, however doesn't make sense to me because

(1) heater core (I believe) has only one air outlet and it is available to both sides,

(2) plenty of hot air is available on right, and

(3) system still misbehaves when heater should not be an issue.

Specifically in regard to (3), when ambient temperature is ~70 degrees F and both sides are synched and set to 65 with A/C off, both sides blow 70 degree air as expected. When A/C is turned on, cold air blows from the left but the right stays at 70. I have some thoughts on this, but would first like some opinions of the community. Many thank in advance to you all.