I thought I heard my name
Sorry I didn't see this thread sooner...
Here's my thinking - only a theory since we probably don't have all the information.
IF the previous owner of the tank wasn't as fastidious about maintenance, the tank may have had a problem before you got it. Inadequate water changes, overfeeding... the nitrates were probably high before you began.
Others have already discussed moving the sand - all I'd add to that is if it had already become a "nutrient sink", it moved the problem from point A (the original owner's location) to point B - your house.
Live rock can also become a nutrient sink - all that stuff for all that time, absorbed into the rock, and now it's continuing to leach out.
If you used original water, that was already saturated with nitrate, you "imported" the problem.
I respectfully disagree with Andyman concerning moving water to "shorten" the cycle. Beneficial bacteria are not usually suspended in the water column, they colonize on surfaces, so unless the water was pristine, or there are other logistical reasons in favor of moving water with a tank, we don't do it or recommend it. And, if the water was less than ideal, there's no sense in moving bad water.
But that ship has already sailed... but it *might* explain why you're having ongoing problems.
Did you happen to test the water before the tank was moved?
If not - no biggie - the tests taken shortly after the move support the idea that there were problems before you got it.
What I would conclude is that your frequent water changes etc., are helping dilute the stuff that's leaching out of the rocks now - while the level is still remaining higher than desired, if you did not do those changes, you'd likely see it continue to rise... so you're going about it the right way, it's just going to be a matter of time until you can catch it and get ahead of it.
The one thing working against you is that while you're trying to catch up to the nitrates, new ones are being introduced (food, waste).
In a perfect world, if you had known about the issues first, you could have re-cured or "cooked" (no real cooking required!) the rock, meaning, you could have tanked it, either in a fishless tank or other vessel, with water movement and protein skimming, to cycle out all the built-up stuff, over time, while doing water changes etc., to flush out the buildup of stuff. Not adding food (or fish poop) to the mix might have caused this process to happen a bit more quickly.
Since this isn't a perfect world, keep doing what you're doing. Small but frequent water changes to dilute.
What are the rest of your parameters? Including phosphate - chances are that's high too because it happens in a 'nutrient sink' situation.
A Phosban reactor would be fine to remove phosphate - OR you could put other media in it, such as Matrix or De*Nitrate, those are biological media that create a favorable environment for denitrifying bacteria - but it's also important to assess whether you may have a phosphate problem also.
Biowheel or no biowheel - that question has sparked much debate over the years. In my experience, "your mileage may vary" - some folks use them with no problems, others have plenty of problems. Popular thinking is that they "create" nitrate. That's not quite right... your system creates the nitrate, but the biowheel is not geared to break it down into nitrogen gas - that's an anaerobic process.
Since you're having problems, I would probably suggest removing it - BUT, first I'd suggest "replacing" it with a more suitable media and running both for a time, before taking off the wheel.
What you saw happen, was likely caused by a sudden decrease in biological filtration and the system had to reset itself to compensate.
I'd suggest putting some Seachem Matrix or De*Nitrate into your filter, with some Stability (soak it first in Stability) - it should fit in the compartment where your filter cartridge also goes (should be room for both). Leave the biowheel in place for a couple of weeks until the Matrix or De*Nitrate starts to become biologically active, and THEN remove the biowheel. The Seachem media has more surface area for the anaerobic process to happen, which is what breaks down the nitrate.
If you have coral frags that don't appear to be thriving, it could be a number of different things causing that, including nitrate, but a full set of parameters might also glean some information. Low alkalinity, pH, specific gravity, and the presence of phosphate can also make things "unhappy".
If you have other parameters at hand, please post them too so we can take a look at the bigger picture.
Jenn