I spoke to Brian at SSK and he said their reamer is good and it is not the chamber. He suspects the Starline brass and said it works with 375 JDJ, but will NOT work with 309 JDJ. He said they haven't tried it with 358 JDJ yet, so I might be in uncharted waters. He said I could send it back, but that'll cost me $20 for postage. I'm trying to see if I can get a loaded round from someone local to me to check. If it works in one SSK cut chamber, but not mine, then I know it's the chamber. Conversely, It could show pretty quickly that Starline Brass is not going to work for JDJ cartridges below .375, which can help others save time and money by not making the mistake I made. Thanks for all the info gents!
But for the grace of God, there, I go.