I've seen, and done, this recipe before, its posted quite widely on the internet.
Firstly, the butter, thats good its in the recipe, taffy usually includes a dairy, and you could even increase the amount if you wanted to. But use a neutral flavored oil for everything else, such as your dish (or if you get a silpat you wont need to oil that), definitely oil your gloves as well as your shears.
Ok, so 260 is your target temp, as for how to get there, I can easily see why there would be different opinions on how to get there. Taffy is normally stirred during the boiling process, this is because, unlike when your boiling sugar for hard candies or for a showpiece, the taffy usually contains a dairy product that should be stirred to prevent scorching, and also has a very high percentage of glucose or corn syrup, which will greatly reduce the crystallization of the taffy. All in all, you can bring your candy to a boil while stirring, then stir every once in a while until you reach your temp, and keep it on that high heat. A low heat will take longer to boil and your taffy can develop a caramel-like flavor, which is usually not desired in salt water taffy, since fruit flavors or typically used. Also, do wash down any sugar crystals that you see during the process.
Thats good you got your candy to come out nicely on your first try! The change in texture after a week is from the sugar crystallizing. In alot of formulas for taffy, you often have almost twice the amount of glucose or corn syrup (by weight) to sugar. This delays crystallization and the candy will keep chewy for a much much longer period of time, so with the proportions of sugar and corn syrup in your formula, this would be a normal thing to occur after one week.
As for your second and third batches, I really would attribute that to a difference in boiling temp. Use one thermometer for consistancy, preferably a probe, not the flat stick looking ones or the cheap glass tube ones you stick to the side of the pan. Be sure, too, that your thermometer is calibrated.
As for your formula, try adding twice the amount of corn syrup as there is to sugar, and perhaps doubling the butter and adding it at the start of cooking rather then the end. Stir the entire time during boiling.
If you want, pm me and I can give you another taffy recipe that may get you started in the right direction.
Edited by Minas6907 - 7/24/13 at 8:07pm