As a biochemist you will enjoy this:
If you are using the API test kit, the 2nd bottle uses two reagents. One is a liquid, the other is a powder that is for all intents and purposes insoluble. So, you need to shake the living crap out of that bottle before using it, and then shake the living crap out of the test tube after using it. Basically, don't trust the reading you get from the nitrate test. It is there as a general guide, not to actually identify a problem. Focus on the ammonia and nitrite levels.
As far as the water change amount, do a 100% water change. The bacteria live in the filter, not in the water. The cycle seems to "pause" after a water change sometimes, but the research I've seen shows that the N-bacs (nitrosoma) prefer much lower levels of nitrite than other bacteria (nitrobacter). The nitrosomas are best suited for trace levels of nitrite (< 0.17g/mL), whereas the nitrobacters do best in levels much higher than that. If your goal in doing a water change is to lower the nitrites, then you might as well remove every bit that you possibly can to bring the levels back in line with their preferred level. Otherwise, just let it go as it is and allow it to fall on its own. (As waterdrop stated about lowering ammonia during phase two, this is also not in the thread on fishless cycling. But, based on the research from Dr. Tim Havonec, it makes sense to try to culture the environment that the nitrite bacs prefer as much as possible, without going crazy with water changes. After all one of the best features of the fishless cycling process is that you aren't required to do a lot of water changes, like in a fish-in cycle. The other benefit, of course, is that you are not poisoning fish during the process.)