Hi
As already said the UV steriliser isn’t likely to kill of your bacteria as most of it will be tied up in the rockwork etc. I run UV(C) 24/7.
Firstly you need to make sure your doing water changes with 0 TDS RODI water as if your not you could be introducing more nutrients to your tank. If you do this, a 20% water change will reduce nitrate by 20% or thereabouts. Don’t necessarily trust what a LFS sells if you don’t make it yourself, test it
So if it were me I would carry out a serious of 20% water changes (so it doesn’t upset the water chemistry to much) over a few weeks and this is the simplest method of bringing the levels down.
Once down you need keep them under control with whatever method you choose. Simple water changes, Carbon dosing, refugium etc....
If the tank is the nano you mention, then I would keep it simple with water changes, but you must use good quality new saltwater