It sounds like you are picking up a lot of heat from the attic.
Anything you can do to get it down under 100 up there, should help out.
If the main source of warming inside your rooms is coming from the ceiling,
you might want to think about adding a reflective radiant barrier up there.
AtticFoil® Do-It-Yourself Radiant Barrier Foil Insulation
Assuming your home is pretty air-tight:
If have a dehumidifier that's not a power hog, you could try running it during the day.
If the air indoors is somewhat dry when you turn on the AC, a better comfort level
will be felt much quicker in most cases.
If your home isn't very air tight:
Or if some of your windows are like these..
You might want to consider a ceiling mounted heat exhaust fan. (Whole house fan).
Which would suck in outdoor air, but would remove the even hotter air
that accumulates near the ceilings of your living spaces.
Whole House Fans — A Scenario | Brian Irwin || Windermere Real Estate Co. ||