Dj!
You just don't know how to interpret this stuff!
In my view you are having a "textbook" fishless cycle and that water change seems to have done just about exactly what I would have wanted it to do! The water change, *most importanly* raised your pH from 6.6. into the 7's, which is your main goal for this sort of water change, to counteract those nitric acids that go along with the nitrates building up at the end of the nitrification process. It also took out plenty of nitrite(NO2) but this just showed that your A-Bac population is looking really good because the A-Bacs swallowed up all that ammonia and dumped out a lot of new NO2!
Your fishless process is going fine because during the first 20 days you were working on having the A-Bacs get big enough to start really dropping that ammonia from the 5ppm, which finally the did, and when they did, they've started doing a strong job of it ever since. Actually, the fact that they are doing so well is what's making the N-Bacs look so bad! The poor N-Bacs are munching away and no doubt growing bigger, but the mountain of NO2 out there and available to them is just staying way above any kind of movement your test kit has the ability to show you. But that's OK! That's what we all see in this "Nitrite Spike" phase like you're in.
Hang in there! Your next milestone of course will be when one day the N-Bacs finally break through their mountain of NO2 and suddenly you find that NO2 is not "off the charts." At that point you'll be interested in seeing that NO2 can be processed in 24 hours and then it will take some time for it to work its way down to processing it in 12 hours.
You have a large tank and a big filter, right? Sometimes they have a stubborn feel to them during fishless but the end results are often very robust. Once you start getting those zero readings you've basically "got them for life" unless something messes up. And once you've got those zeros, you've got the basis for a fantastic environment for your tropical fish. (Consider the alternative! Fish in there and getting readings of ammonia or nitrite... you'd have to desparately be doing those large water changes perhaps every day!)
OK, so for now, while the nitrite is spiking, you really don't need to be recharging all the way to 5ppm, you can do 3ppm or so and there'll be plenty of ammonia to keep the A-Bacs maintained ok and not have them pump out quite so much excess "N" compounds. Once the N-Bacs have "caught up" then be sure to ease it back up to 5ppm before the end.
~~waterdrop~~