Hello; Yes to the water changes. My take at this point is that you have something going on in the tank. Water changes will, at the very least, dillute the toxin in the water as long as the toxin is not in the tap water itself. The prime is supposed to make the tap water safe with regard to the chlorine/chloramine. With the conditions you describe water changes of more than 20% should be considered. If you are using the new prime then massive water changes should not be a problem. It seems that you really have little to lose with a series of big water changes at this point. Whatever the actual issue may be, the water changes should not hurt.
I have been thinking under the notion that ammonia is the culprit up to now. The new ammonia alert is reading that the water is OK for ammonia, right? Lets do some more detective work in case there is something else going on.
Things such as 1) Are the buckets and such used for water changes used for anything else? I have dedicated buckets for my tanks. No household cleaning or mopping. Is there anyone else around your place that might use your tanks buckets for mopping or such?
2) Can anyone have put something in the tank ? Drunk friends, an angry lover or such.
3) Have you added anything to the tank? At this point the stuff pictured in the center of the tank could be removed. Some things can leach toxins into the water. Did you glue the stuff together with anything?
4) Do you handle chemicals at work or in other hobbies that could still be on your hands?
5) Have you changed the food or checked it out during this time?