kkid--by now I'd bet you're getting pretty frustrated--both with the problem at hand and the solutions and answers being provided, trust me most of us have had frustrations like this at some time or another. At the risk of complicating matters I will give you my opinion of what to do.
First I TOTALLY agree with broomer here. Some may disagree based on the stress factor and the risk of changing the water paramiters so drastically at one time. However I believe this risk is at least equal to or less than the risk of letting the 160 nitrates continue.
Broomers ideas of the seperate tank would be best. But I personally wouldn't want another tank running, so, considering you're fish are on the hardier side anyway here's what I'd do.
1--remove fish into buckets (inverts too.)
Also save a bucket of tank water
2-drain that tank down to about a couple of inches above the dsb.
3-Then replace with fresh mixed water.
4-add powerheads to aerate and mix, and replace skimmer.
5-remove filters, throw the cartridges, and place bio-media (floss sponges rings whatever else into that reserved bucket of tank water.
6-clean the actual filters out, you can use fresh water for this. Include a brush for cleaning inside tubes and such, don't forget impellers and whatever else.
7-By now your tank should be fairly mixed, check the sg, temp and ph to ensure equal to old water.Adjust if neccesary.
8- return filters to tank fill with tank water replace the bio-media (that has been rised in that old tank water) and new cartrideges and get them running.
9-begin acclimation process of fish and inverts by adding approx 1 cup of tank water to their buckets about every 15 to 20 min. Continue to do this till their buckets are just about full. Total time should be at least 3 hours. (this acclimation will be longer than a normal one due the extreme change in nitrates levels.
10-Check you tank levels once more before putting your fish back in.
11-start building your live rock collection, one piece at a time, remembering that with each addition it's about the equivalent of adding a fish and your system will need to adapt.
This is the first step in my opinion--
After that, while you may have been under the impression that too many water changes was a bad thing, I disagree with that. Monitor your levels and do them accordingly. Every tanks needs are different, and your tests will tell you what YOUR tank needs. Do the filters at each water change at least.
After that just relax, test and wait. Eventually I think you will be able to lose your powerfilters and go filterless if you want, but not until your "natural" filters are WELL established. (imo-about 1 year.)
This may or may not have been what you wanted to hear, and I may get in trouble from other members but I really think it may be your best bet for now (later is a different story)
Good Luck