As part of your experiment you should get as many test kits as you can for the known supplements so you can test the water over time. You should be able to pinpoint which elements your tank uses up more readily than others. I figure you could probably do your method for a year or maybe even two before you would need to scrap the water and start with a fresh water change.
I didn't change the water in the 75 for a year, and had great growth with the CA reactor. I may have just convinced myself to buy a new reactor since the TE are coming from dead skeletons... In fact, that's probably the difference, in the wild corals are built over themselves and I am sure there is some kind of breaking down of the old skeletons which replenishes the TE for new growth.