Hey Dave, if a tang is acting weird in that small of a tank its very more than likely the tank is undersized for the fish. The clowns however have been known to host in sand, powerheads, magfloats, you name it. I'm not sure what makes the tang want to stay near them but I would give him up to the LFS or a fellow reefer.
For your LFS to give you an unncessary fish to fight algae.. well it may make the problem worse not better and isn't the best advice I can think of.
If I may interject - nitrates (and phosphates) tend to be associated with treated tap water instead of good clean RO\DI water. If you are using RO\DI look to your feeding schedule and what you feed. If the fish are creating a lot of waste despite your water changes it could be the problem, especiatelly if you're feeding pellets and flakes versus frozen. I have in personal experience found a correlation with dry preserved food polluting the water parameters a tad more than strained frozen food.
Another quick thought- are you making sure the tang is getting his veggies despite whatever territory issues you may have?
Back to the water params- when you do water changes you may see a little bit of difference if you take a clean turkey baster (dollar store is usually a good place to get) and use it to "dust" off your rock. 60 lbs is quite a decent amount for that size tank and without a lot of good strong flow or direct dusting, some particles get trapped in your rock and essentially fester and pollute the water.
Other than that double check your bulbs aren't old for your lighting schedule and that you just aren't overfeeding in general and hopefully one of these things will address the algae issue more than putting a fish that poops a w hole heck of a lot in a smallish sized tank to eat.
A good tip on feeding- tangs are pretty good munching on algae all day long but for the other guys try using a good frozen mysis shrimp (you can always add vitamins if you wish and garlic) and remember that a fish's stomach is about as big as its eye. If your clowns are young yet they may only need to get by on 2-3 mysis shrimp. Compare to that to what you feed now and see where you register in.
Maybe we can kill two birds with one stone with your water quality and the tang
