+2 on verifying that the test kit is correct. Red Sea has a good write up on their algae management product on the various methods of removing nitrates and phosphates. According to them:
Firstly, Vodka dosing should not reduce PO4 and if not combined with a PO4 reduction method, your N P ratio will get out of whack and lead to cyano outbreaks - doesn't sound like this is the case for you.
Vodka dosing with sugar and vinegar will rapidly reduce both N & P, but you risk H2S forming; this is toxic. Also rapid reduction of N&P can destroy the zooxanthellae in your corals.
The bacteria that consume N & P with carbon are complex - each doing different things and producing different results - good and bad. This is, I think, why gradual reduction of N&P on balance is needed.
A refugium accomplishes this, but according to the red sea article, you would need a sump equal in volume to the DP to achieve the nutrient export.
I am not endorsing their product N03-PO4 - X as I have never used it. For now, bio pellets, a skimmer, and a cheato packed fuge (plus 15% water changes) are bringing my N&P down steadily (to the point my the cyano is under control). I will say that the logic they use to justify their algae management product appears to be working in my case.
It's about providing the right nutrients in balance for the different bacteria to do the safest reduction of N&P, but not in a way that will destroy the zooxanthellae in your corals.
Fwiw, I have an overstocked tank and a LTA did great (and got too big from my 30gal). I introduced a red BTA last week for my ocelalris (not the best match up, but I put them together in a floating breeder box and after 10 days, I was delighted this morning to see my female appears to finally be taking to the BTA). I tested yesterday before a long over due water change and my N03 was at 2PP and my PO4 was at 0.08ppm - NO3 down from 3 and the ratio of 25 much closer to my target of 16.
Note on testing - for a year I was testing NO3 and PO4 with API reading 0 on both. But my tank observation was telling me it could not be correct. Last month I switched to Red Sea's test kit and sure enough, I was making decisions based on incorrect numbers.