Thanks PinkDiamond for the info!
You're so welcome! It's awful when the little guys get sick, so I'd love to be able to offer some help!
Here's a link to instructions for salt baths:
I've never done salt baths on my betta, so I can't comment on whether or not being moved in and out of the tank is stressful. I have however used aquarium salt in my bettas tank when he had ripped fins and he seemed to do well with it! Just remember to dissolve the salt fully before adding it to the tank or making a salt bath solution, and when I added it to my fish's tank, I did so gradually to acclimate him to the change. I felt like that would reduce his stress. The salt in itself is supposed to have a soothing effect for the fish, balancing electrolytes for stressed fish, aiding with gill function and preventing some types of bacteria from developing.
Another point to consider, though you may already be onto this - from what I understand, Bettafix/Melafix are only antiseptic, not truly antibiotic. The active ingredient is tea tree oil, almost exactly the same stuff that's in human skincare products (very slightly different formulation for the fish, I'm pretty sure). So if the Betta/Melafix isn't working, that doesn't mean that the fin rot would not respond to a true antibiotic, if you need to move on to strong medications. There are also antibios for fish that will treat different things than what the JFC targets, so it might just be a matter of finding the right meds.
Anyway, hope some of this is useful to you! Hope your boys are recovered super soon!