Personally, and some will disagree, I would use the chiller as a back up solution only that won't run every few days. I keep my temp at 81.5F and my SPS, Soft corals and LPS are great. I've been running this temp for many day and the "general" degree for ocean is around 80-82F and yes i undestand that some of the ocean is warmer and cooler, but generally it's 80-82F.
Use fans and you can also raise the bulbs higher off the water's surface. what lights are you using? You need to find the heating factor. If you ever have a pump go out on the chiller and your tank gets to 88F without it, then you run a high risk of killing a lot of live stock because more then likly it'll be a huge temp swing.
Another thing that could be causing the heat is your room temp. When i didn't have any A/C (from Oct until yesterday) the temp would hang around 80F as my room temp and couldn't bring down the temp any lower then 83F using fans. I can live with that, but if you don't have that circulation, it could increase the temp by quite a bit. Without the fan the temp would get well over 86F and i quickly attached the fan after only 1 of my MH bulbs turned on.