I don't think any of those three things are significant.
The amount of iodide in salt is pathetically low (from the standpoint of health), and will be oxidized to free iodine in a few minutes.
Stranded or straight wire, no difference except when you try to clean it.

As for the sodium citrate, they were probably all made in the same plant at the same time. Often, different grades are just subjected to different tests. Its like semiconductors: the manufacture runs off a batch and tests them, then puts a different part number on them depending on how good they are.
The big thing with gold is the amount of salt. It controls how much gold you are going to get. With silver, each hydroxide will combine with a silver atom and make silver hydroxide. With gold, it takes 3 chlorides to combine with the same gold atom to make one gold chloride. However, there is no guarantee that three chlorides will find the same gold atom. So a lot of the chloride is wasted, I think it bubbles off as gas. After that, you are just electrolyzing water and the citrate.
Anyway, its the fact that gold has 3 valence electrons that make it more complicated.