If your home's HVAC system was designed properly, and I'm not sure the new homes these days are, and you have proper attic insulation, you shouldn't have hot and cold rooms. The duct dampers are there to make small adjustments.

The only thing I can add is If you are going to replace your HVAC system get a Variable speed Inverter system becasue it runs more than it is off and will equalize the temperatures in all your rooms. With a conventional system it's 100% On or 100% Off so it might not be running long enough to push enough air to the problem rooms if the ducting was not designed correctly. In mine and others who got these variable speed systems, the air temperature consistency across all the rooms was vastly improved.

I find that impossible unless you are A/Cing you garage when it 95 outside, so you’re saying your garage is at most 75 degrees in heat of day? My garage has insulation over it and faces North northeast. Maybe 5 or 6 degrees less outside temps in heat of day.

My garage faces to the southwest and the doors are insulated. This reduces the long wave radiative flux off the garage doors by quite a bit. Regardless, the garage typically runs about 5F above the outside temperature in the afternoon.

OP have the technicians check the actual ducting. When we moved in 15 years ago, our north facing master was always hotter than rest of house. Went into the attic and found strapping holding up duct had broken and duct had dropped. Created a kink allowing less air flow than other rooms. At that time we were able to call warranty and they had someone come out and restrapped all ducting. No further problems.