Of that 10ppm+ nitrate reading I'd question two things:
-Test kit accuracy. Color comparison kits are tough to read sometimes down into the double digit ranges. You might be reading 5-10 ppm off in either direction. I have used them on my systems, and I mainly just try to get that kit to read zero. Whenever there is some pink on the test strip line, I make the water changes more frequent.
-Rock dieoff not yet done or feed/waste accumulation. If there is nitrate, it is coming from one of these two sources considering your water change frequency. You can identify the source by temporarily removing some of the rock and placing it in circulated saltwater in another smaller tank to concentrate the water volume. If rock dieoff is the source, you'll get ammonia readings in this test system and that should be quickly detected. If this is the case, the bacterial populations in your main system are sufficient to convert this rock-emitted ammonia into NO3 which you are measuring. Make sure you have no pockets of feed or waste built up into the rocks, maybe this happened at the fish store too>?
--If you shake your rocks underwater or move them to a cleaning buckets and get a lot of grit and mud in the water, or any type of clouding, this material is likely protein and detritus accumulations which are feeding your nitrate stores.
-You can't go wrong with a skimmer if you don't mind the space usage. Anything that removes waste is helpful!