OP stated that tech didn't measure airflow so it was ASSUMED he didn't have the tools. We all know what assume is so lay off the tech please. The fact is most tech's don't measure it if they don't feel it is necessary. Nothing to do with what equipment they have in their arsenal.
Apparently I missed the word "apparently" in the Op's statement. Maybe I should have worded it differently. Not trying to pick on tech, but just trying to advise he may need someone who is better qualified.
I would not outright replace the ducts as shown in the pictures, either. I'd do a some rerouting and stretching of them, and install balancing dampers on takeoffs to the rooms.
Without being onsite to evaluate the system, I'd say the standard lazy duct run installation is resulting in too much air emerging from outlets near the air handler, with outlets further from the air handler either being nominal or starved. Clean up the overall installation and it may be better balanced, prior to installing dampers (which are still a good idea for balancing purposes).
Goes to show that words on this forum can often fall short of really describing the situation. Even pictures have limits, but help. Only an onsite evaluation can really nail it.