It's not uncommon for nitrate to go down slowly(sometimes it takes months) when starting out with high nitrate .
Perhaps the bacteria are using ammonia directly for nitrogen and it takes a little longer to get at initially high nitrates in those cases.
Maybe lower phosphate is limiting the bacteria in some cases . 0.02ppm to 0.04 ppm per the Hanah 713 works well for me; .00 ppm per the Hanah is lower for PO4 than I would prefer in my aquarium. and might indicate aphosaphte deficiency.
FWIW, I reduced nitrates (from the 80ppm range to near zero ( somewhere between 1ppm and 5ppm, IIRC) with a sulfur dentirator, intially;water changes on a smaller system might be more practical.; waiting it out might be ok too.
The organic carbon dosing dropped nitrates even even lower after the first few months . They've have stayed low,usually around 0.2ppm for the last 5 plus years with organic carbon dosing( vodka and vinegar in my case).
Providing a little phospahte might also help accelarate tne nitrate redcution in cases where a trure inorganic phosphate defieciency exists. I think those would be rare in a tank with food going in unless some aggressive PO4 removal was in play