The salt works by dehydrating the fishes skin, in turn sort of drawing the parasite out.
I think it is literally impossible to dehydrate a fish's skin since they live in water. Also, the ich parasite is not vulnerable when it is on the fish's skin. It is only vulnerable when it is in the free-swimming stage. I'd suggest you review the info in the link you provided, the Skeptical Aquarist's site.
Salt works because it stresses all the organism in the tank. It stresses the fish, the plants, and the microorganisms. What you hope to do is achieve a level of stress that kills the microorganisms like the ich parasite without killing the fish. As the fish are a higher order lifeform, they usually can survive a little more stress than a microorganism.
This actually is kind of how most ich-specific medicines work, too. They are poisonous to everything in the tank, but usually worse for the ich organisms than the fish. The formalin mixtures today are blends of formaldehyde and methalyene green. Both of which are poisons, but the blend of them lets each of them be used a much lower concentrations and still be effective in killing ich. The heat treatment also follows this philosophy: stress everything in the tank with heat, hopefully stressing the microorganisms to death before stressing the fish to death.
A big take away from the above is if a fish is sick or infirmed in some way other than just the ich, the stresses in trying to kill the ich may also kill the fish.
My suggestion would be that if you want to try the heat and salt method, I would be sure to have medication on hand just in case. There are strains of ich out there today that are tolerant of much higher temperatures than in years past. And, if the fish are showing high stress, you probably will want to scale it back and try a medication.
And finally, learn from the lesson here and understand how important a quarantine tank is. With proper quarantining of every single that that will go into your tank, there is no reason your tank should have ever gotten ich or any other disease. Quarantining works if done. Otherwise, you run the risk of situations like this where you're going to have to treat the entire tank and risk all the inhabitants.