You shouldn't try to keep SPS until you can test Alk, CAL, and Mag. If you say your SPS dies overnight, if your alk is very low you'd have a ph drop at night which would kill your SPS. No idea if that is your issue, but try testing your PH in the middle of your light cycle and again in the middle of the night to see your fluctuation... You already say you're using Salinity, which is a great salt, and if mixed correctly gives you perfect paramaters. You need to test Alk and CAL daily for at least 1 week in order to calculate your depletion ratios. Then you can properly calculate a 2-part dosing schedule. With salinity and a good water change schedule your Mag should stay in line around 1350. After that I would say to start with the easiest SPS like orange monti, green birdsnest, and/or green slimer. Don't try the more delicate SPS until you are sure you're system is ready.
I really don't think the temp swings are the problem. In the summer i've had my system fluctuate from 78-82 in a day while out of town with no ill effects on SPS. On the great barrier reef during low tide SPS will sit completely out of the water with full exposure to the sun...