Worse comes to worse OP is out like $5.00 in carbon and goes the UV route if still unhappy. I'd bet money that a small bag of carbon like chemipure would be enough for a tank like this+1
In a 13.5 UV IMO is overkill. You can general control such a small water volume much easier than a larger one. UV on a large tank would be much better seeing as doing a 100% WC on 13.5G vs 100% on 200G is like trying to move a car with your hands and rope vs driving.