The water conditioner just removes the chlorine and a few other nasties from your tap water. The ammonia problem is due to the concentration of ammonia in your water. As you have done a complete water change, it should be down to 0ppm until you add the fish back in and they start producing more. BUT by doing a complete water change, you will have lost most of the bacteria that break down the ammonia, so if you left it now, the levels would skyrocket again, so you need to do daily partial waterchanges to keep the concentration down. In time, the bacteria will multiply enough to be able to break down all what the fish produce, but until then, lots of partial waterchanges I'm afraid!!
Large water changes should have very little effect on the bacteria as the beneficial bacteria is in the filter, not the water.
OP, you need to test your ammonia every day (twice a day) and do any large water changes needed. This may mean 80% water changes every day for a while. You also need to test nitrite as nitrite comes from the ammonia.
There are products that remove ammonia but they are not advised for these kinds of problems. Zeolite, if used carelessly, will starve the beneficial bacteria in your filter and stop your tank from becoming balanced. Ammo-lock will give you misleading ammonia test results so you'll never know how toxic your water is.
It's good, old fashioned water changes all the way.