I should have explained that more thoroughly.
DI resin absorbs ions (charged particles dissolved in water) out of water as water passes through the resin. Resin doesn't pick certain ions, like nitrate for example, but it absorbs all ions. The resin continues to do this until it is full/exhausted.
Your saltwater is about 35 parts per thousand salinity. This means that about 3.5% of your tank's water is salt (ions).
If you pumped your tank's water through DI resin, the resin would absorb ions out of the water. But the resin would become full/exhausted almost immediately, like way before you saw any reduction in nitrates.
Chaeto works okay, but it won't work miracles. There are other things you can do:
Water changes are the most efficient, but are expensive on large systems.
Carbon dosing. Do you have a good skimmer?
Remote deep sand bed.
Feed less.
Edit: what is your nitrate reading?