I have heard of ppl running only algae scrubber in their system but never heard of ppl running only chaeto. Maybe can infer?
I suggest if you are really interested in additional nutrient export, start off with chaeto and run for a few months. If you are still not satisfied, then worry about how to set up an algae scrubber. It's not as simple as running chaeto in sump. Also need to take note, for a relatively bigger tank like yours, you need a substantial amount of algae/chaeto for the setup to work.
But since your tank is starting up, I would also recommend not to use any of these first and see where tt brings you to. Maybe you don't even need to employ any of these methods.