I have found the API liquid test kit to be very inaccurate when testing for high levels of nitrites. It seems to be really good at measuring values between 0 and 2 ppm. But once you get above 2ppm, you might have a reading as high as 20ppm, but the test strip might only look like it is still 2ppm.
As others have suggested, you need to do some huge water changes.
The other thing is that I seem to recall that when doing a fishless cycle, at some point you need some potassium (or something else, don't recall what) to help get that 2nd bacteria that converts your nitrites established. Basically, I recall reading that if your fishless cycle stalls, try adding just a touch of fish food, as it will contain the potassium (or what ever element is needed) to help get the cycling moving along.