Salt alone doesn't do anything. You use the alcohol to soften up whatever gunk is in the pipe and the kosher salt absorbs the gunk as the alcohol evaporates. If you're going to try the S/A treatment, make sure that you pack the airway with a couple of pipe cleaners and rest the pipe on a slight angle so that the alcohol doesn't run out through the bit. You can ruin the finish if alcohol comes in contact with it. Fill the bowl with kosher salt and drip in just enough alcohol to cover the salt. Leave it for a day. Once the alcohol has evaporated tap out the salt.
You can also just try cleaning out the airway. Get some bristle cleaners, dip them in alcohol, and swab out the airway. I would use the tapered variety, inserting the thicker end first, and using a combination of back and forth motion coupled with rotating the cleaner. You might just let the first couple of cleaners rest in the airway for an hour or so before scrubbing the interior. Some of the alcohol will work itself around the tenon and soften any residue.
If the cleaners come out dirty, continue until they come out clean. Finish with some dry fluffy cleaners. Gently try to rotate the stem. If it doesn't move, give the pipe a day or more to dry out before trying to remove the stem or use the freezer method again.
If the stem doesn't respond to treatment, send the pipe to one of the repairmen that have been recommended.