Sick Rummy, any ideas?

[PNWaquarist]

About four days ago (Tuesday evening), I noticed that one of my younger Rummynose Tetras had tattered fins and was paler and more lethargic than the others. I assumed that this was fin rot or some other type of bacterial infection, and my LFS recommended API Furan-2. Before beginning dosing (three days ago), I did a 30% water change. Per the instructions, I did a 25% water change after the first two doses and added the third dose last night. I have one dose left to go (tonight), but could dose again once more after that, if needed.

In the pic of my sick Rummy taken just now, there's a healthy one below, for reference.

In addition to the tattered fins (note the white coloring of the fins near the body), the fish's color is pale overall and its gills are pumping more rapidly than usual. It can swim about OK, but spends a lot of time by itself near the heater or close to the substrate. It hasn't eaten since at least Tuesday.

This Rummy and its seven friends were added to the tank a little over a month ago (acclimated for 45 min, with 1/2 cups of tank water added every 15 min). Since then, I've added 4 Sterbai Corys, 8 Cardinals Tetras, and 7 Black Neons. Outside of one Cardinal who may or may not be in the early stages of fin rot, the rest of my fish seem fine. The tank is 29 gallons and I'm using an AquaClear 50 filter with some additional Fluval peat pellets to darken the water with tannins. I do 20-30% weekly water changes, with Prime. The fish were originally fed Ocean Nutrition Community Flakes, but I switched them to New Life Spectrum Small Fish Formula 0.5 mm sinking pellets two weeks ago.

Other parameters:
77 Farenheit (steady)
pH 7.3-7.4
GH: 3 deg
ammonia: 0 ppm
nitrites: 0 ppm
nitrates: 5-15 ppm (usually ~7-12 ppm)
Tank is moderately planted and has a bogwood "cave". Lighting is a 17 W T8 bulb.

Based on the picture and description, does anybody have an idea of what (besides fin rot) may be affecting this fish? It seems to me that there's probably a secondary infection, but I have no idea what it may be.

Thanks in advance.

 

[PNWaquarist]

After doing some more reading and not seeing any improvement in the fish's condition (it didn't eat today), I decided to euthanize it. I suspect that, in addition to fin rot, it may have had either Neon Tetra Disease or False Neon Tetra Disease. It very well may have been the bacterial version of NTD, as the fish had been visibly affected for at least four days now (and possibly longer, if I had looked closer). My understanding is that true NTD will outright kill most fish in a few days. Mine had at least another day left in it, if not another one or two after that.

Nonetheless, I couldn't risk exposing the rest of my stocking to NTD. I certainly wouldn't want to wake up one morning to find a cory picking at its remains. Interestingly enough, the diseased fish was added to my new tank on the first day of stocking and was apparently healthy for a good four weeks. Thankfully, none of my other fish are displaying symptoms. (Knock on wood.)