Wouldn't matter how much nitrate you add to a tank that is over the limits on copper, the coral will still die.. Even worse it will polute the tank and accelerate the die off. There are 2 fish at least and a clean up crew in a 18 gallons of water that's plenty enough coral food. I would try to get some zero tds water as soon as possible as and do a 50% water change. Your triton results won't be back for 2 weeks and your coral will most likely be dead by then.
I am not discounting the possibility of copper from the distillation process. However you ARE discounting a nitrogen deficiency.
Your take on Nitrates is totally wrong. Adding 2.5ppm will neither "pollute" the tank or accelerate the die off. Obviously if the OP is running 0 nitrates, that he has an effective removal source. 2.5ppm will likely disappear overnight due to a surplus of DOC. (Dissolved Organic Carbon). It's likely that surplus that's driving the bleaching event. There is a real simple test to see if it is nitrate deficiency, add nitrates and maintain a couple parts per million. If the RTN STN/bleaching event ceases and the coral begin showing signs of recovery in a few days then it was a nitrogen deficiency. If it doesn't stop the event then you don't have to dose anymore, you can check that off of your list of possibilities.
In the meantime you can wait for your triton test results to see if there is heavy metal contamination and address the issue! I totally agree 100% GET A NEW SOURCE OF WATER.
It amazes me how many aquarist are resistant to adding an ionic form of NO3 but have no problem squirting mystery bottles of amino acids, and "trace elements" into their tanks on a regular basis.