You are very dedicated, good. Still it would be nice to se a chromatogram, preferably a LC-MS. You dont learn so much from this NMR-study, its mostly confusing.
Yes, why do you see the iodide? Thats key, it should be consumed. If you used the sulfide as nuchleophile and then oxidised to sulphone you would get fast and more clear result I think. You could even do this one-pot.