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.