Iodine is tricky. Have you read up on Dr. Holmes-Farley's iodine articles and FULLY understand them? You probably have plenty and they don't test for all kinds of it - this is the most likely scenario if your shrimp molt and survive and you do change some water. There is elemental iodine, which is probably what they test for, that does not do much. There is also Iodate, Iodide, some with some + and some with some -. It can be dangerous if you add too much. Be careful here. This is where I am saying that the "data" says low iodine, but the "information and knowledge" should caution you to look further. You could be raising iodide levels beyond what is good while all the time testing low for something completely different like elemental iodine.
I would at least figure out EXACTLY which kind of I that they tested for. Our local place does ICP for elemental iodine and not iodate. I have no idea what they test for (each is different) and you could be on the money, but worth a check since you dosing a poison into your tank in large doses. Halides are one group that I would not add without acute testing.
Chaeto can easily diminish iron, which might need dosed even if you change water - it is growth limiting in low concentrations with a lot of macros. This is not as dangerous as iodine, so you can probably do this without much testing.
