I'm terribly sorry for your loss. I know you cared deeply for that fish, and tried your best to help it. Not many of us go to the lengths you did to save it; going to a vet,
an hour and a half away, too, was above and beyond the call.
I agree it looks like it could be fungus, but I don't see in the pics the long whispy hairy looking structure that is characteristic of saprolegnia. It's probably the camera, but it looks more filmy and dense, fluffy but not hairy looking. Is that what you see? Or do you see the hairy fuzz?
You said, at one point, it looked like strings coming off of the fish's body, could it have been copious amounts of slime coat? Just wondering.
If that were the case there could have, in fact, been a parasite infestation as your vet suggested. If so, I don't know why he/she didn't address that with the proper recommendation for an antiparasitic.
As Cerianthus stated, a necropsy could be very helpful, both to you anf to all of us, if you're up to it.
Again, I can't tell you how very sorry I am for your loss. This was a fish you had for a long time and it is obvious that you cared very much for it and did your best. I hope the knowledge of that will bring you some measure of comfort.