G'day,
I really think you have to take this "cycling" business with a grain of salt. Understandably, you're going to want the most suitable tank for your axolotl, which obviously means a cycled tank.
There's really nothing wrong with having an ammonia level of 4ppm (only during the cycling period, of course!), as long as your axolotl isn't in the tank, hence, the 'fishless cycle'. In fact, I think you may be prolonging the process by doing these drastic water changes. If the ammonia concentration does not creep above 4ppm, then you should be fine. It is only when ammonia goes above 4ppm that will have to perform partial water changes to keep it down. Generally speaking, you'll find yourself with a perpetual nitrite-spike should the ammonia level go above 4ppm.
How long have you been cycling your tank? Hopefully you are aware that this process can range any where between a few weeks to a few months. Nonetheless, there's no rush. The process is also different amongst individuals. For instance, I never enountered nitrate in the so called ammnonia >> nitrite >> nitrate phenomenon. Also, what method are using to test for ammonia?
Personally, I'd just let the tank cycle without the axolotl in it, but that's just my 2 cents. As ammonia toxicity is of greatest concern right now, I'd put the axolotl into the fridge while the tank cycles. You could put the axolotl into your other fish tank(s), but you'll have to factor in the possibility of transferring disease(s) to/from the axolotl/fish. And, as always, the axolotl could eat these fish, or worse case scenario, the fish kill your axolotl by meticulously nibbling at it making it more susceptible to pathogenic invasion.
While the tank is cycling, I'd monitor the ammonia and pH ensuring that ammonia does not creep up above 4ppm, and pH does not drop below 6 because both discrepanices will hinder the nitrification cycle. Word of warning though, do not use any chemicals or powders to boost the pH. Let nature take its course.
As mentioned earlier, if the ammonia goes above 4ppm, perform a partial (20%) water change. In doing a massive water change, I believe you'll be getting rid of what ever bacteria colony is trying to form, and also any organics that are trying to adhere to any surfaces. Bacteria seldom remain in free water, but they'll start off some where there and then adhere themselves to surfaces that contain organic matter (i.e. food). This process is known as chemotaxis. Therefore, if you are continuously disturbing the tank, these organics don't have the 'chance' to adhere to the surfaces and, thus, attract a colony of nitrifying bacteria; which leads me to my second point. It's not a good idea to stir the sand all the time because aerobic nitrifying bacteria will be residing a few millimetres below the surface of the sand. But this is not to say that you don't stir the sand every now and then to get rid of pockets of hydrogen sulfide.
If, however, you're still keen on starting over, here are some pointers that I've picked up along the way (mainly through the wisdom of others, and also through trial and error):
- Remove the filter from both tanks before you start siphoning out any water. This will prevent any debris from being transferred along with the filters.
- When removing the sand, try to carefully siphon the upper most layer because this is where the aerobic bacteria reside. Don't mix the upper and bottom layers of sand together. You can place the upper layer back on top once when you've added the bottom later again. NB. make sure you keep the upper layer with just enough tank water to cover it.
- Try to keep all your decorations/plants (basically everything in the tank) wet, i.e. don't let anything dry out because you'll be losing that precious biofilm.
That's about all I can think of. I hope I haven't confused you in any way

Good luck!
Jay.