You dont have to many vents going on I have about 8. With 2 of them larger (10 inch for a large area). Do you get good airflow coming out of them???
I think you need to look at optimizing the setup, most air cond people dont have proper understanding of the engineering principles mainly behind airflow etc. I have seen many setups that can be improved. Even with my own system I spent many days after work modifying it to work more efficiently.
in regards to your setup,
I would be checking to see if firstly you have correct airflow can you at least feel air coming through the vent when the lovers are pointed to the flow??. Check return air filter is clean and that the path to the unit it unobstructed. If it isnt then there are options in a setup menu to increase the airflow of the unit.
If airflow is ok then I would be checking to see if the air is coming out cold enough. You will need two thermometers for this. One near the return air and the other at the outlet. You should be achieving a 10degree difference after about 20 - 30 minutes.
You also need to ensure you do not have direct sun coming into the room you are trying to cool down.