Need advice on really long fishless cycle. The problem - lack of nitrates

Looking good so far.

Yes, it is normal for nitrate concentration to go up really quick near the end of the fishless cycling. The good bacteria in your filter is so sufficient at converting ammonia and nitrite. It is a good thing. Once you have added fish, their bioload will not be as high as the amount of pure ammonia you have been adding to your fish tank, unless you severally overstock your aquarium with too many fish. So the nitrate will never go up that quickly once you have added the fish. Once a week partial water change will be enough to keep the nitrate low.

Your fishless cycling is over as long as you no longer get a reading of ammonia nor nitrite 24 hours after you have added up to 5~6ppm (2~3ppm is totally fine too) of ammonia. You only need a few days to confirm it is really over. Then you are ready to get your first batch of fish.

A few suggestions. It might be a good idea to add a background to your aquarium. Something green or black. It is entirely up to you.

For the number of cardinals, you can get more of them without a problem. They are not messy fish, and they will do better in larger number.

I look forward to see your fully stocked aquarium.

Good luck!