Removing your carbon won't really do anything for your nutrient levels. I would recommend feeding your corals more, or feeding your fish more, or at least dosing amino acids if you do not want to increase your nitrates at least slightly. Phosphates may be another area you should measure. If they are super low, you might want to increase those as well (run less gfo if you use it or feed more...foods have phosphate in them).
In general, I think there are two type of low nutrient systems. You have some people who may not feed their corals, or they have low stocking levels, and / or they have outsized or numerous nutrient exporting mechanisms that are extremely (too) efficient at stripping everything from the water. These tanks I'd classify as being "sterile" almost.
The other type of low nutrient tank, which I find preferential, are the ones where people are feeding their corals (or at least dosing amino acids if nutrients are staying low), or they have higher stocking levels and feed the fish more, but their corals bacteria, etc. and their husbandry and export mechanisms are still effectively keep nutrients at undetectable levels. There's definitely nutrients being supplied daily in these situations but readings may still register 0 on test kits because an almost perfect equilibrium has been achieved. As such, if I were going to err, I'd rather err on the side of having at least some nitrates and phosphates being registered versus virtually 0 numbers. My nitrates run as high as 10 ppm and my phosphates have been as high as 0.30, which is 10 times higher than the 0.03 number you read about all the time. I don't think my numbers are ideal, but I just mention them because I was always led to believe that nutrient levels like this would kill corals or cause massive algae outbreaks. I don't think that's the case at all. However, this doesn't mean that levels don't matter. 100 ppm nitrate would concern me greatly. 20 ppm might indicate an issue in nitrates rising and not being controlled adequately. 2 ppm to 5 ppm I think would be great for lps corals.
I think if you increased your nitrate (and possibly phosphate) to get some slight readings you will see some improvement in your corals. Just my best guess. I've also had perfectly "seemingly" healthy colonies that have grown for years suddenly start to decline for no good explainable reason (like a duncan coral I grew from 2 heads to probably 40 and then it just started dying one day).
Good luck! Be sure and give an update later if you discover anything that helps. That's how I learn on these forums is reading about other people's experiences, both positive and negative.
