The only thing you might achieve by removing and treating the visibly-infected fish is perhaps preventing a few more batches of new parasites dropping off that particular fish and adding to the parasite population of the tank. You can't treat the fish, since the white spots on it are embedded parasites which aren't vulnerable to treatment. The only stage of the life cycle that is killed by treatment is the free-swimming stage that emerges from the cysts after they drop off the fish and sink to the bottom. This is why, as stated multiple times by multiple posters, you must treat the entire tank.
Was the "right salinity" the absolute minimum suggested as a treatment? Perhaps a slightly higher concentration might work? If you are on a drip system, that would begin to decrease the salt concentration in your tank immediately, so if you add only the bare minimum it will quickly drop to a suboptimal level. Either shut off the drip system, or add more salt than required. You'd need enough in the tank so that after 24 hours of dilution by the drip system the concentration is still higher than the minimum requirement, and you would need to add more salt daily after calculating how much is lost daily to the drip.
Ich is a PITA, but it is one of the most easily cured aquarium diseases out there. Sorry, but it just seems extremely unlikely that your tank, alone out of many thousands or millions, has developed some new super-Ich strain that doesn't respond to proper treatment. It's more logical to assume that if the bug persists, then the treatment...perhaps for the reason I mentioned, perhaps for some other reason...simply isn't being done properly.
Also, as stated earlier, the parasite is easily transmitted from one tank to another by wet nets, siphons and other tools. Disinfecting this stuff in a bucket of weak Betadine solution or similar is an easy and effective way to limit tank-to-tank cross-infection.