Interesting problem. Here are some ideas.
1) Whenever there is an odd nitrate test result, you always have to consider whether the test rests are misleading, e.g., the test was done incorrectly, the sample was contaminated or there is nitrite (NO2-) present.
2) How fast is nitrate being produced? Does a large water change decrease the nitrate concentration and then it slowly increases? Does skipping a day of feeding decrease the nitrate level? Is there just more nitrogen being imported by food than exported?
3) 20 ppm nitrate for 125 gallons of water corresponds roughly to 160 g or about 6 ounces of biomass (wet). Are you missing a fish or two?
4) Bacteria absorption of nitrate can be inhibited by the presence of ammonia. Said another way, the bacteria you are feeding with carbon might be competing with the ammonia oxidizing bacteria in your tank for ammonia. The idea is that until the vinegar consuming bacteria become ammonia limited, nitrates will be untouched. Consider increasing the dose of vinegar or decrease the feeding for awhile. I have seen suggested upper limits for vinegar of 1 or 2 mL per gallon per day or when the water becomes cloudy or the presence of excessive bacterial growth on surfaces, and 0.5 mL per gallon per day as a maintenance dose. I have also seens reports of coral issues, presumably through some sort of interaction between carbon dosing and high alkalinity, but this interaction has not been validated. Similarly, there are claims but not validation that cyanobacteria outbreaks are caused by carbon dosing. Cyanobacteria outbreaks seem to occur randomly.
5) A one year old UV lamp performance has probably substantially degraded. Also, is the dwell time in the UV time correct? The UV unit just might not be a lethal device any longer.
Dan