Most water conditioners do not remove nitrIte - I believe Amquel Plus does, and there may be others - but most just do chlorine, chloramine, heavy metals. But the bacteria in your filter should be able to cope with the nitrite long-term. In my (limited!) experience, they're quite slow to kick in, and take a few days to reduce it to zero after a blip.
As Corleone says, if you do a large water change, you'll just be adding more nitrite from your tap water. Large water changes are probably best avoided unless the nitrite level in your tank gets higher than in your tap water.
I have nitrite in my tap water, so I do twice-weekly small water changes (about 10%) - this means my nitrite levels never get above a trace, but I'm still refreshing the tank water. I'd suggest that's probably the best solution for you, to do frequent small water changes (you might get away with less than me as your tank is more mature), and make sure you don't over-feed or over-stock. If it becomes a problem, you could consider RO water, but that's extra cost and hassle...
Hope it sorts itself out soon, and good luck with the plecos.