This assumes, of course, that you're trying to simulate Fox Talbot's early work. Indeed, he did use NaCL early on but was unhappy with the results (he tried several methods to varying degrees of success). Herschel came up with Hypo (now known as Sodium Thiosulfate) as a means to permanently fix out the excess silver and passed the info on to Talbot (Herschel was very involved with many of the early chemical processes). Both Talbot and Daguerre switched to Hypo when it became clear that sodium chloride was not up to the task.
In answer to the OP. Sodium Thiosulfate is the fixer you want to use. As you've already noticed, Ammonium Thiosulfite is far too active for many of the older processes. Salt prints, Albumens, and VanDykes, all work best with plain Hypo. For VanDykes I use 1 heaping tablespoon of Hypo crystals to 1 quart of water. Works like a champ!
Who else are we trying to simulate, he discovered the process. In terms of Salt Printing, which was originally discovered by Fox Talbot, I would suggest this is not the best advice. If you read notebooks P and Q you will see Sodium Thiosulfate was introduced for the Calotype. You are indeed correct in saying that sodium chloride was not up to the task. However, if you read between the lines of Talbot’s notebooks, you will see that even after the more practical process of complete fixing, he returns again and again to salt for its aesthetic value.