160ppm nitrate suggestions?

[FitoPharmer]

I am taking care of a large ~350 gallon system. Initially the tank did not look good, I found out the top off water was being badly contaminated with copper, and there was copper just sitting in the tank from a brass float valve. Since removing the copper and doing a large (~100G) water change things started to perk back up. Since the fish were showing signs of HLLE and other illnesses I inquired to their feeding situation. They had been feeding frozen food and freshwater flake once a day, and sometimes nothing over the weekend. They also are not currently turning off the return pump for feedings. I told them to feed twice a day, and gave them some algae to feed the tangs. The HLLE on the blue tang looks to be getting slightly better and the white spots on other fishes disappeared but then I noticed the anemones were not as happy as they should plus the nitrates on the dip tests they had went from 20-40ppm. I then decided to try a test with my nitrate kit, which showed 160ppm. I am not shocked at all, other then how poor the dip tests work, since the system has an ancient filter system. Bio balls and filter floss that are never cleaned, no skimmer, no fuge.

My question relates to the fact that I have never had such a a large tank in this situation. What is the cheapest and most effective way to lower the nitrates ASAP? A decent skimmer and carbon dosing schedule comes to mind. But I am also thinking about a macro fuge / ATS in the mean time since the tanks budget is pretty tight, and most of it was just used on a new ATO, controller, filter socks, and food. I will be talking to the building manager on Monday to see what can be done for funding.
Is there anything else that I am not thinking of?
I am also going to be instructing them to go back to one feeding per day until the nitrates are under control.

Any help or suggestions would be appreciated.