Well the Birchwood Casey Perma Blue 50/50 with tap water worked the best for me. I was going for the not browned, not blued, but more of a raw not shiny steel look. Cleaned the barrel with brake cleaner, dried/wiped down, applied the mix in uniform passes along the length of the barrel, rinsed with tap water, wiped dry and used fine steel wool to buff out to a slight steely look then used Kroil and steel wool on the entire barrel again then wiped clean. Looks good. The mustard took longer and wasn't as reactive as I thought it would be (maybe brand, French's) plus it just made me hungry for one of the old salcissia in a pretzel at Gus's in St. Louis.
Anyway, thanks all for the anecdotes/remedies/et cetera.