Can't keep nitrates stable

I've had some problems with high nitrates and started tackling it with some Purigen which worked fine but the moment I start feeding my corals with BRS Reef Flakes the nitrates spike and it takes DAYS to lower. First I went from 160ppm to 80, then to 40, then 20 and it settled at around 2-5ppm until I started feeding again. Now I'm back to 50ppm. I don't have a sump and it's not possible for me to add a sump to this system so a refugium is off the table. It's a 40g tank run with a Sun Sun canister filter and one hang on Nano skimmer (rated for up to 35 gallons). The skimmer doesn't really pull out that much gunk. It's a white foam and slightly yellow skimmate so the only main source of filtration is the canister filter and the rocks/substrate. I need a way of controlling nitrates and keeping them stable. Even water changes won't do anything. Actually, I want to stop doing water changes because every time I do a 10% water change my corals seem stressed. I use RO/DI water. Does anyone know what I could do? Maybe bio pellets in the canister filter? Vodka dosing? Zeovit system?