I agree that water softener salt can have additives, but it is generally 99% pure salt, of which very little actually gets into your system. I have measured salt levels extensively over the past 10 years, and have found that using softened water usually results in a .1% salt concentration in the pond (point one percent, or one part per thousand).
Softened water has no effect on KH. A high KH with a pH of 8 or even 9 shouldn't be a problem, healthwise.
You mentioned you had rain. Are the mules smaller than the Koi?
I tend to agree with luvmyasagis. Gill flukes or KHV.
Muck on bottom is not good, but don't think that one of the symptoms of Hydrogen Sulfide poisoning is gill bleeding. Necrotized gill tissue, maybe. Lots of parasites can hide in the muck, though.
However, it has been a long, long time since I've had any bleeding gill issues... could be missing something....
I hope you get to the bottom of it.