Dropsy is not, in and of itself, a disease, but a result of disease, illness, or poisoning, which causes some type of internal organ damage and failure which then results in accumulation of excess fluid in the tissues and abdominal cavity.
Dropsy is usually due to the failure of the kidneys and/or liver. In humans, and other animals as well, heart failure and diseases of the lungs can be a cause of dropsy, so probably this is true of fish as well, so they are correct it is not a disease but an end result of disease or poisoning.
Having read many of your threads and posts, I know that you carefully monitor and manage the water in your tanks so I have been reluctant to believe that the problem has been a result of water quality issues on your part.
It could be true, certainly, that something else from the municipal water supply could be causing a problem, such as more chlorine or chloramines in the water than you are dosing for in the tank.
Or, there could be some other source of toxins in the water which could be having the affect of damaging internal organs thereby resulting in dropsy.
lf one of those scenarios were the case it would seem more logical to me that most or at least more of the fish would be displaying symptoms of dropsy at the same time, instead of almost one at a time.
Having dropsy progress through a succession of fish in your tank seems more to be a result of a disease producing bacterium in the water.
I've read that the bacteria that produces columnaris, for example, can exist in a less virulent form in a tank, so there is not a massive epidemic that sweeps through the occupants, but rather, a more insidious, slowly moving process that infects the fish individually as the health of their individual immune systems dictate.
I think you do have some kind of disease producing bacterium in your tank, though I would explore the other possibilities regarding water contaminants. You could call your water department to ask if there have been increased levels of chlorine and chloramines. Also, check to see if anyone in the house has used any chemicals near the tank, or sprayed anything that might be harmful in the air in the same room.
I read a post in which someone had used an airosol fabric deoderizer, FeBreeze I think, that had caused serious problems, some deaths if I remember correctly, in their tank.
I know you know all of the dangers of contaminants, though. You've been doing this for quite a while and are an experienced fishkeeper.
Just trying to think of possibilities.
I still believe that the problem is an infection. If that is the case, continue with the antibiotic treatment. You may need to sanitize your tank and equipment since some bacteria are very tenacious. If you do wipe out all traces of illness by means of antibiotic treatment of your two tanks, then you will kill your biofilter, but you can start over cycling your tank again.
I think I'd watch the tank. Keep up the antibiotics. Keep water quality pristine. Check with the water department. If your fish improve and you have no further cases of dropsy and hopefully have some of the fish with dropsy get well (which is very rare, once dropsy has set in) continue on the assumption that you are treating a bacterial infection.
Keep us posted on the progress. Photos would be helpful.
Further advice can be offered as we see the direction things are taking and also what steps may be necessary regarding the disinfecting of your tanks.
I'm hopeful that we may be able to get more insight and advice from more folks that have a lot of experience with disease and/or dropsy.