, if you are interested in some light reading, this thread
should do the trick.
Summary, we were trying to determine if Seachem Matrix was actually generic pumice stone that was specifically sized (pretty much is). As the experiment grew, we decided to see just hard hard you could push the 2 products - very surprising.
Then the experiments moved onto plastic bio balls, Fluval brand bio media, Eheim bio media and finally a sponge filter. Think I even tested a canister filter with absolutely no bio media or filters. All products could be successfully cycled within a predictable amount of time.
One of the more interesting observations - I could push most of the products to accept over 40ppm doses of ammonia (yes, that amount is correct) and within 24 hours I would have 0ppm ammonia and 0ppm nitrite. The down side was the nitrate levels went so high in 24 hours that I had to do 100% water changes before I could add a different amount of ammonia and test again (the high nitrate levels, i.e. over 200ppm would stall or limit one or both oxidizing bacteria's).
Not that any of the above would help your situation, but there is a lot of good information throughout the thread. I believe at some point there was a calculator or spreadsheet that allowed me to sample the tank water, get an ammonia level, the figure out exactly how much ammonia to add to achieve a desired level of ammonia. In your case, it sounds like the first part of your cycle is complete (growth of ammonia oxidizing bacteria). I did find that when growing the ammonia oxidizing bacteria, it helped to keep the tank warm (80 degrees ish). My tap water measures 7.6ph so I never had any ph issues. My GH is 11-14 depending on the time of year and the KH remains pretty stable at 7-8.
Interesting that your ph dropped significantly lower than your tap/source water - don't have enough info to answer why that is. Your heavy water changes should have resolved that issue (raised the ph). Something of note, in order to feed the nitrite oxidizing bacteria, you first have to feed the ammonia oxidizing bacteria. 4ppm daily ammonia levels (not necessarily dosing) worked well when growing ammonia oxidizing bacteria. Once I achieved that step, then I went with around 3ppm ammonia daily dosing to keep the ammonia oxidizing bacteria alive. This did result in fairly high levels of nitrite for awhile. I don't recall doing many or any water changes during this part of the cycle. If I remember right, the nitrite oxidizing bacteria took about a week longer to catch up.
Once you achieve a completed cycle, the ammonia oxidizing bacteria will double in size in less than 24 hours (closer to 12 hours). The nitrite oxidizing bacteria take longer to double in size - closer to 20-30 hours.
What all this means in a practical sense is your could setup a 5 gallon bucket on the back porch (or a 10 gallon tank like I did), hook up your canister filter (or HOB / sponge / what ever) and cycle the filter. Once cycled, you can increase the beneficial bacteria colony to match water ever size tank / fish load you are planning on having. Example, you assume you will need a filter that can process about 4 ppm ammonia in a 80 gallon tank.
4 ppm in 80 gallons
8 ppm in 40 gallons
16 ppm in 20 gallons
32 ppm in 10 gallons
It's all the same amount of ammonia being added on a daily basis (either by fish or you). The only difference with the 10 gallon tank is your have to do water changes to keep the nitrates at a reasonable level.