Fair point, I forgot about the size of the system, sorry about that.
I like Privateye's idea. Macro algae reactors, biomedia reactors, reverse flow deep sand beds, and other solutions might be able to help a bit. It depends on how much you can fit in your sump. You can also try to get a second or simply larger skimmer if possible. The more dirt you get out, the better.
The more tedious option would be to rinse rocks you can take out in a bucket with tank water to get rid of a lot of detritus that is just decaying and releasing nutrients. You could also start replacing the substrate in small batches, which is another detritus trap. Adding some dead dry rock in the sump if you have space left can also help by offering more surface area for beneficial bacteria. There are many small improvements, but nothing will immediately bring your nitrates down.
If your tank is running fine, you might also be able to simply ignore the nitrate readings. If you read through
Randy's article on nutrient target ranges, you will see that many very good-looking tanks have very high nitrate levels and seem to run without any problems.