Its not easy to exactly pinpoint the culpit(s).
When you say your softened water, is pH of that soften water lower than tap water? It should be when softened.
As long as
no Ammonia (
NH3), Nitrite (
NO2), would continued to do routine (25-30% weekly) small water changes with softened water until pH of tank is stablized around neutral UNLESS testing reveals otherwise..
When pH goes too low, youo may want to mix soft/hard water to do water changes.
Anytime when NH3 is present, raising pH is the worst thing anyone can do to fish. Keep that in mind.
As far as One sick fish, cant recommend any since not sure if and what it maybe suffering from. Isolating is good idea if and when possible. If separate container is unavail, you can use large hang over the rim pastic container (one that lfs use to catch and hold fish to bag). You can hang these container inside the tank to isolate the one sick fish. If suspect fungal infection, can treat that one sick fish in container with Aq salt/med (proportionate amt to container volume of water) thus no other fish are exposed to unnecessary med.
I know it is lot of work & gadgets but these gadgets will come in handy down the road.
When NH3 and NO2 is NOT registering, you have not lost/disturbed biological bed.
Liquid test is better way to test water than Strips so think of investing in
API F/w Master Kit (around $20 online).
I just wish i can assist more/better. Hope tank is stablized soon.