Feel free to ask as many questions as you like on this topic. Since my Rainbowfish contracted TB and infected all 3 tanks, I am actively working on the Fish TB problem.
I suspect your Neons have TB. Fish TB is very common in tropical fish hobby. One study found that over 80% of the 300+ tropical fish examined had TB. Fish were from both home aquariums and pet shops. I'm speculating that the fish selected and autopsied were dead, dying, or moribund.
Fish TB is incurable. What's more, the usual measures, in my humble opinion, make it worse. I went all-out to feed my fish (for a month) with Rifampicin/Ethambutol (key antibiotics used for treating human TB). Did not work.
What's more, I think treatments and cleaning measures backfire. Mycobacterium species are all incredibly slow-growers that dominate clean environments. Some have been found in bottled water! They don't last long outside the fish in a dirty environment where they have to compete with much faster-growing, normal bacteria.
Last summer, one of my Turquoise Rainbowfish had a small TB sore on her side. I put her in a hospital tank containing salt and antibiotics. The sore only got bigger. I put her back in a regular planted tank with lots of dirt. The sore has totally healed up, and she's doing fine as I write this.
I too thought I'd have to tear down tanks and start over. However, since I added UV sterilizers in Jan 05 to the tanks, my fish stopped dying. They seem to be doing well.
The UV sterilizer will kill the TB bacteria released by the infected fish. My fish are probably still infected, but they're not being continuously exposed to more Mycobacterium in the water. As with any pathogen, the number of pathogens that the fish is exposed to is critical. The UV sterilizer lowered that number to a level that the fish's immune system could handle.
This is all tentative, folks.