Well, I don't think incomplete rinsing was the issue with my yellowed cotton T-shirts using grated Ivory soap. I used a Neptune 7500 FL with the extra rinse, and the loads were generally small, so plenty of volume and sloshing going on. I also used STPP so soap scum likely didn't happen either. Although I suppose if I tried it again, I'd add some Oxyclean, which might prevent the yellowing. But I have no plans to do so. All my whites now are done with in a Miele at 160F, using Sears Ultra/Oxyclean/STPP combination detergent. They come out sparkling white and soft, with no need for fabric softener.
I still may try the Zote flakes anyway, once I can set up to get to Walmart early in the morning on a weekday to avoid the hordes. I have a couple other Walmart-only items I need to check out, anyway.