I started my fishless cycling about four weeks ago. I have had one set-back where 60+ of my 140 gal fishtank overflowed and I replaced it with city water...probably not a good idea as my cycling was clearly harmed. Now, two weeks later, my nitrites are staying at zero, or close to it, but my ammonia remains around 4.0, even though I haven't added any ammonia. Also, I can't seem to get my Ph above 6.4.
In summary, my Ph hovers between 6.0 and 6.4 ( I use Ph UP and I've added a 1/4 tsp of lime twice), my ammonia stays at 4.0, nitrite at .25 or less and nitrate at 80+.
See if you can get some different things to test and see if the tests give you different readings.
I'm also curious about your tap water pH.
You can go to ace hardware and get some hydrated lime and mix a spoon full of that with water to get a faster pH adjustment. If you can also get some potassium hydroxide (old fashion lye) you can raise pH while also getting potassium into your system Beware both these are caustic so be careful with them. I wouldn't raise the pH all the way to 8 though. If you get it up close to 7 that should work. I've noticed that systems cycled up at a high pH often experience ammonia spikes again when the pH drops.