You will have to carefully consider your approach. I know it seems like animals are so much more valuable than plants, but...
If all of your Neons are infected, and since it is a deadly disease, you will probably lose some or most of them anyway. I am not sure if Rams and Corys can die of NTD, there might be other things involved here too.
Anyway, what I am saying is: don't tear down the tank and throw out all plants. If you have a quarantine tank, you can separate the apparently sick fish. If not, I would leave things go its own way. Don't add any fish. Don't think about getting Neons ever again. Just wait it out. Focus on the plants, on your aquascape, fertilizers, CO2, light, etc. Have an eye on water parameters. Often fishies become more susceptible when they are under stress, which could be caused by many things. Water conditions being one factor.
I have a few times introduced sick fish to my tank (don't try that at home
) with ich and apparent fin rot, and not only didn't they infect any other fish, but got healthy pretty quick all by themselves. (On the other hand a while ago I lost a Ram that seemed healthy, but got thinner and thinner and finally disappeared completely). I am getting more daring now, until the lucky strike ends and my entire tank gets wiped out :hehe:
Adding an UV sterilizer might be a good idea...
Keep us updated... there are always some ideas floating around here.