You have an unusual situation. Most of us trying to diagnose an SPS STN/bleaching problem don't have another tank on the same system where the exact same colonies are doing very well.
Given that's the case for you, you've eliminated 90% of the water chemistry and nutrient export questions that need to be run down in the case of poor SPS survivability.
This is what I'd suggest. Don't alter your photoperiod, since you have SPS that are doing very well. Instead, remove 2 of the 10 bulbs in the ATI fixture. Or raise the entire fixture by another 10" off of the water. That will drop the intensity of your lights somewhat, and perhaps give the acros in your frag tank a chance to adjust to the main display.
One other thing to check - since you frag tank and the DT are on the same water system, there's really only one thing that could be substantially different between the two tanks - temperature. You might want to measure the temp of the DT very closely, particularly near the end of the photoperiod just to make sure that your tank temp isn't over 80 deg F.