Post your location and one of the pros from this board may be close to you. Finding a contractor to help resolve air flow issues can be difficult.
Doing the blower door test will provide you with good data. Sealing as much of the duct as you can will help overall in getting the air to where it needs to be. Use mastic to seal. Installing a booster fan is normally a waste of time and money. Installing a mini-split will most likely fix the issue, but cost more than should need to spent to resolve this.
Since your duct work is accessible, adding dampers should be easy. Balancing the system after the dampers have been installed and they know how much air is needed in each room should not take very long either. It took about an hour or so on my system.
Thanks for the offer, but I think I'm going to give the original HVAC company a chance to make a recommendation and possible changes.
I'm asking here first because there have been a few things they did that I haven't been happy with, and wanted a little more knowledge so I could evaluate whether I think they are steering me straight or not. I think this is probably their last chance though, before I look for someone else.
You have young children and it is not good to leave them sleep in a cold room.
I agree with you this needs to be solved:
1. Mini-split is basically a combination of small compressor (outside) and evaporator+quiet fan inside, with both of these componente joined by refrigerant line. Just google mini-split and you will see what they look like.
This is available in:
- AC only
- AC + Heat (through heat pump concept).
However Minisplit can cost you $3-4 "arms and legs" (part and labor included per my HVAC Co).
Since you are above garage, I guess the "outdoor" unit can be placed inside the garage. Your HVAC tech will have to drill through the garage ceiling to install the refrigerant lineset.
Since your room faces North, you will have COLD issue in the winter but not HOT issue in the summer.
2. Another option is "Baseboard Heater":
Then buy a separate wall thermostat to control the heat.
You need an electrician to run a 220V line from the Service Panel to that room. The electrician should be able to do that without tearing much drywall.
(Is your Service Panel close to that bedroom?).