Before you do anything else, or spend any more money to solve this problem, I would strongly suggest you contact a home energy auditing company and have they perform a full home energy evaluation
Home energy audits are really inexpensive worth every penny because instead of looking at individual systems, they look at the home as whole.
They will usually include a blower door test to see how much air leakage your home has, and a thermal imaging test to see if there are insulation gaps in the building envelope or just overall poor R-Value insulation. They will check your ducts for leakage, as well as your attic and your foundation - the two main areas of concern when it comes to insulation and air leakage.
Truth is that no heating and cooling system will be energy efficient if the air that you are paying to cool and heat is consistently leaking out or if the temperatures from the outside are influencing indoor temperatures due to poor insulation. These conditions make any HVAC system work more than they should.
The U.S. Department of Energy states that you can save up to 30% in heating and cooling bills with proper air sealing and insulation.
Here you can find some more information on air sealing:
Air Leakage | Air Seal a Home for Energy Savings | Air Sealing Info & Service