I would also bring up yet a different possibility that has nothing to do with the cooling system itself. Rather, I’d guess that you are having an issue with your blend door. This is in the ductwork and controls the air path in the ducts. Many of these are vacuum controlled, and the engine vacuum varies as you do thing like accelerate. I used to have a Caravan where the air went to floor vents anytime you accelerated, no matter where the position was set. It would go back to where you put it after accelerating. I’d start by looking along the firewall for a disconnected or damaged vacuum line. If nothing is found there its time to go fishing under the dash.
Of course, it might also be that your blend door is solenoid controlled in which case I’d be tempted to ignore what I just said.