The thing that would concern me there is that you say some vents are blowing little, while others are fine. I doubt that is a cleaning issue. And the expensive company quoted replacing at least part of that duct work stuff. Why? Did they show you problems? If it's not done right, then having it done right could make a big difference and improve the airflow. it's not unusual for installers to hose this up in new construction. Sometimes just adding a couple returns can make a big difference, especially on the second floor.
You can probably buy a cheap inspection camera or rent one if you want to see what the inside of the ducts look like. But i'd bet the low airflow isn't dirt, more likely just longer runs, more bends, ducts that are too small, etc. You should examine what you can see too. Not unusual for ducts to be held together with duct tape, instead of the good metal foil stuff. It dries up, then a joint leaks or falls apart entirely.
You might be better off getting the guy you just had back, giving you a quote on the replacement after he's taken a good look at the whole thing, what's right, what's not, etc. And call another vendor or two for quote on replacement, show them the airflow problems and ask them what they think is wrong, how it can be fixed, etc.