It is made to run. I live in Austin, and until 9:00, that compressor will be buzzing away.
My recommendation are similar to the above:
1: Reflectix in the windows. There are insulated "pillows" which are made to be shoved into skylights and vents. You will have to take your pocketknife and make a slit for the crank.
2: Turn the A/C on early in the morning, so it isn't trying to catch up all day.
3: Run fans. Ducted A/C is good, but a couple "O2Cool" fans will even further distribute the air.
4: Check your line voltage. If it isn't up to spec, consider an autoformer.