As far as CUC goes. Nothing will touch them once they get that long. Snails IMO mostly stick with film algae. I have had better luck with hermit crabs for hair algae bc they plug out the "baby sprout hair algae". Again once the hair algae grows long, critters don't like them anymore.
You can't detect any excess nutrient bx the algae absorbed it already.
Manual removal, daily, as others pointed out, and keep it up for a month. Dont starve your tank. Keep the nutrients up and by daily manual removal, you are forcing ur system to find an alternative natural path for the nutrients to go. Nutrients have to end up somewhere. And right now your current system doesn't have enough "alternate" nutrient absorbers (bacteria, filter feeders like sponge, corals, etc) that have reached enough biomass to outcompete algae (bc algae is the easiest and most efficient ansorber). By daily manual removal and upping your CUC (which will help cut back on the new baby hair sprouts), you give these other absorbers a chance to reach that critical biomass to help keep algae in check.
If space allows, get a fuge and a good grow light or a ATS. That is another direct competition against algae growing in your tank and who will win that competition will basically boils down to which side has a bigger biomass (so don't start with a small gulfball size of chaeto in the fuge if the DT has a full head of hair algae) and light. I always say "one strand of hair algae growing in your fuge is one less growing in your DT.
Dosing live phyto will also help turn the competiton against hair algae, and your corals and pods will love it.
You don't need chemicals or miracle bottles. Those tend to upset the balance and stability in your tank and unstable conditions make algae grow faster. What you want to achieve is that balance and natural control and competition to keep algae in check. A little elbow greese and the multipronged competiton against the hair algae listed above and you should see positive results in a month.