Are you sure there are no NitrAtes? When was the last time you checked? I just read back on your old cycling post and noticed you did have ammonia to start with and now it's gone. That's a good sign usually. Did you ever show signs of nitrItes or nitrAtes? If you had nitrItes and they are now gone as well as the ammonia then I would say your tank is cycled. If you've never shown nitrItes then it hasn't cycled. You need nitrItes to help create the beneficial bacteria. Or at least that's how I understand it.
I pinched this from another site I'm a member of:
The purpose of cycling a fish tank is the production of "good" bacteria that eats the ammonia and nitrites that kill the fish. Ammonia eating bacteria is called Nitrosomona and the bacteria that eats the nitrites are Nitrobacter. They grow in your filter media. Having these bacteria's are what is known as a cycled tank.
A cycle basically goes -> Ammonia to start -> Ammonia & NitrItes -> NitrItes & NitrAtes -> and finally just NitrAtes.
Hope that helps somehow...
As for your filter. If I read right you've got carbon and sponge in there. I would probably only add something like aqua clay or ceramic rings. One Axi in a tank that size won't produce much ammonia. I would only put the zeocarb back in once you're certain the tank is cycled. It's good for removing other things from your water as well, not just ammonia.
I started all my tanks out originally with sponges (coarse and fine), a standard filter carbon and something that assisted in the retention of beneficial bacteria like aqua clay or ceramic rings. I did regular water changes, DID NOT clean the substrate or filter until it started cycling, Only then did I clean the substrate every second water change. My ammonia eventually turned into nitrItes and then into nitrAtes. I only clean my filter when it becomes noticeably clogged or I notice a problem with the water quality. They recommend cleaning your filter using tank water as tap water usually has chlorine and chloramines in it which can kill beneficial bacteria. I actually clean mine in rain water as that our main source of water where I am.
Cycling can be so confusing when you start a new tank. It can take so long for it to happen. But it does happen. Just keep a close eye on your water parameters and your Axi and it will eventually happen.
I have six tanks running and the whole cycling process drives me nuts sometimes. LOL!!
In saying that, I'd better be off. Today is tank day and I still have a 2ft to clean and water change.
Good luck!!