Nitrates are produced from the breakdown of organics. Many other compounds are produced by this same process. Some of these other compounds can be highly toxic, even at fairly low concentrations, and are hard to test for. We concentrate on nitrate simply because it's easy to test for.
So, even if nitrate, in and of itself, is not highly toxic, many of the other compounds that can potentially come along with nitrate can be very toxic.
Every system is different. The rate at which a particular compound is broken down, changed, or removed from each system can vary wildly. A system that maintains high nitrate levels, without adverse effects being detected, is NOT evidence to exclude nitrate concentrations as evidence of overall tank health in ever system. Sanjay Joshi may be able to maintain high nitrate levels with seemingly healthy corals because his system is efficient and processing or removing other compounds or elements before they reach toxic levels. That does not mean every system has this capability. All it takes is the accumulation of one toxic element, like a heavy metal, or one compound like hydrogen sulfide, which can both be released into the water from the breakdown of organics, along with nitrate, to cause major problems for corals.
The ICP test concentrates on elements. Leaving out organic compounds. So even if the test comes back showing everything they tested for being within acceptable ranges, it leaves out a whole multitude of potential problems that were not tested for.
The OP's system has high nitrate and phosphate. Both of which are produced through the breakdown of organics. Combine that with poor coral health, and it's not much of a leap to suggest something's wrong with the water. Even if we can't put our finger on exactly what that problem is.
If it were my system, I'd do as TitanCi suggested above. Do a LARGE water change. Maybe a few LARGE water changes. Then I would reevaluate the system to determine why the products of rot and decay, organic breakdown, are accumulating within the system.
JMHO
Peace
EC