How big of a swing in salinity will kill SPS corals.

I doubt you would see big problems with die off. Just think about all the corals that go from lfs tanks into private tanks every day. They all have to adjust to new salinities, and if done over some time (usually not even as long as you're talking) they do fine. The problem you may run into is that sps growth is slower during acclimation. I've seen this period last for up to a month before the coral was adapted enough to the water conditions enough to really take off. I'm not saying that this is caused specifically by salinity, but it is something to consider if you notice that your future sps isn't growing well. An ato is one of the cheapest easiest and highest impact upgrades that can be done to a system.
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I accidentally dropped my tank's salinity from 1.026 to 1.021 over night once about 4-5 months ago. I lost one SPS coral out of about six in my tank... it was already not doing well, and this sent it over the edge. The rest of the corals were pretty resilient, and are doing great. So, a salinity change of .001 will not kill a coral, but you want the most stable environment possible. You will want to try to minimize that swing as much as possible.