2 thoughts:
1. Sounds like you have a balancing problem -- if you have too much airflow in one area and not enough on another, he needs to look at the overall airflow balance first. This sounds like a system design/installation problem, and it is something your guys should fix.
2. If that gets fixed and the AC still can't keep up, do the insulation. HVAC systems nowadays tend to be sized for the smallest unit that can meet the heating/cooling demands, because it is better for the unit to be able to operate at a fairly steady-state vs. cycling on and off all the time. If your house doesn't have insulation, you may have gotten a "standard"-sized unit for that size house, but that is actually undersized for the heat load.
So there are two ways to fix that. The "normal" approach is to yell at your HVAC guy for undersizing your unit and make him install one that is a lot bigger. The efficient, Mustachian, environmentally-beneficial, long-term cost-effective approach is to insulate the house to decrease the amount of cooling needed to a "normal" amount that your unit can handle (also make sure you have an attic fan). Added benefit that this will cost you significantly less over the long term in operating costs.