I have never felt the need to use ICP tests, but I can see why you want to do this. You can get such tests from places like BRS or even from Amazon. A search will turn up several options for the testing. Most of the test involve taking some water samples and sending them in to the companu. The cost is about $50.
Since I have never used any of them, I can't recommend one over the other. Because this topic did peak my interest I did a search on "best icp test". Giving the results the "5 minute, all inclusive, in depth analysis" it seemed most people thought the test they used was the best.
I wonder if it would also be a good idea to test some newly mixed SW and the water your using to mix you SW. I could see where such testing would give you a base line, and show if the issue was from the new SW itself, or something in your SW system.
I'll also say the STN could be caused by something other than the water parameters. This could also be a bacteria or other infection killing the coral.