What color are the fish's gills? We talked a bit about this in:
 http://www.guppylog.com/story/2005/2/24/163511/736

It is even possible that something in the house is impacting the tank. For a couple of suggestions see

http://www.guppylog.com/story/2003/11/15/55646/798

Do look to see what your three-year old put in. Probably nothing is there. However it is sometimes amazing that any of us or our pets survived that age when we (and our children) suddenly became so mobile and curious and klutzy. I learned fast not to take a 2.5 year old to the hardware store with all of those neat little bins of pipe fittings. ;)

By the way, Melafix in a tank too long, can cause a pH plunge. If it has been there well over a week, start changing it out.

The same applies for salt. A little can be a tonic - especially if there are visible spots or growth on the skin. Too much can dramatically raise the water's TDS (total dissolved solids) and that can lead to trouble. Too much of a sudden shift between waters of different TDS can lead to osmotic shock.

See http://www.guppylog.com/story/2004/1/31/5655/54195

If the fish had flukes, they would probably be scraping themselves on the gravel, rocks or what ever. Did you see any of that?

If you are really worried about them, treat with an anthelmintic or one of the commercial Parasite Guards or de-wormers. That also takes care of several possible (and nasty) internal worms too. I'm almost to the point where any new fish from commercial channels will get that treatment while in quarantine.

By the way, it may be best to leave all the tank paraphernalia in while medicating for parasites (both crustaceans and worms). That way anything adhering to the equipment by surface tension stays   and gets treated.

By the way, kudos to you and you pet shop for using an apple snail to cycle the tank. I think that's neat! If you are medicating for worms, you really need to also include the fry and yes, the snail, even though it could threaten the snail. Remove the snail after 4 days, it should still be ok.

I'm really impressed with what you are considering, even if it is not possible (logistically speaking) to diagnose the disease. Also impressive, is what you seemed to have gleaned from this site, other sites and people and books elsewhere. You are checking for things a lot of aquarists would not know to check for. You may be correct, that lab work (s0metimes within 30 minutes of death unfortunately) may need to be done to actually determine the cause(s) of death. You were not long-winded, just doing a great job of doing your best to describe what has been happening.

Much of this noise from me, admittedly, is just "throwing things against the wall to see what sticks." Sort of like with auto and computer repair, sometimes that's what one must do. :(

You mention treating with your customary water conditioner. Does that treat both for chlorine and ammonia? The reason I ask is that water departments has been increasingly putting both of those in. Indeed they have been asked to do that. If you are treating with just a dechlorinator and they are shipping chloramine (chlorine which naturally bonds to ammonia), you are releasing the chlorine, but also creating an ammonia burst.

Another problem with tap water is where the tap water was very cold. As it warms up rapidly, bubbles can form on the side of the tank - oh yes  - and in the fish's blood vessels. That is a gas embolism and roughly the same as when a diver gets the bends. That is also called gas bubble disease.

Recently visited a cichlid nut (with a zillion gallons of water) and his own well. He is constantly running new water into his tanks with a very fine and powerful nozzle. When asked why, he noted that if he didn't do that he got the bubbles all over the tank. The bubbles were "free nitrogen" and could replace oxygen (or prevent the absorption of oxygen)  in the fish. He said that he first noticed that when he just ran the water into a tank. The fish got a little loopy, just lazily cruising around, sometimes going near the surface. Then they slowed down and died after a day or three. When that happened he was quick to call around and get that nozzle.

That lethargy can also be a sign of nitrite poisoning. The scenario can unfortunately be much the same as with the above paragraph. (And the cure is to do more partial water changes with safe, seasoned water.)

All kinds of stress/ shock - temperature shock, osmotic shock, chemical shock , pH shock and on and on - can be caused by suddenly moving fish from one type of water to another which is dramatically different. That probably is not what happened to your fish. But just to check, did your shop have you add a little tank water to your bag (or jar) with the fish in them? Did they have you then pour off some of that water, 20-30 minutes later, and add some more tank water. After a third time of decanting/ pouring off water and adding
tank water, did they have you throwing all that water out and (gently) dropping your fish into their new home?

If your library has the
A-Z of Tropical Fish Diseases and Health Problems
By Peter Burgess, Mary Bailey and Adrian Excell
(Howell Book House, NY, 1998 or 1999).

Or

The Tropical Fishlopeadia: A Complete Guide To Fish Care
Also by Bailey and Burgess
Also by Howell Book House, NY but C. 2000

they go into this in even greater detail.

If your library doesn't have those books, check their holdings computer to see if either are in a nearby town or if you can get them through inter-library loan. (Your tax dollars at work.)

It may be that you will never know what had hit your fish. It may have been something before they got to your home and you are just now seeing the results. With lots of TLC, your survivors may do just fine.

Hopefully, other than take a little of your time, the above has done no harm and may be a little helpful. Please give a quick mental check though of the scenarios suggested. Hopefully they will all be discarded. :)