wow 7-8 ammonia levels are the problem. Don't let it get over 1 ppm. It's fine to stick your axoltol in the tank when it hasn't fully cycled, but do waterchanges. Even if you have to do it every day. Don't worry about ph, as long as it's not off the charts high. You don't have to have a filter, I would recomend having something to add water circulation. i know you said your axolotl hated the airstone, but are you sure it was the airstone? I have a pretty powerful air pump and mine don't seem bothered at all, just stick your stone in a corner or something. It'll help pump oxygen in the water, and move it around, which is good for cycling. Seriously though, test your ammonia every day, and I would do a water change if it's over .5 ppm's. What I do when I'm cycling is if it's any color other than 0 it's time for a waterchange.