Hey Sudsmaster
Am surprised you find Tide w Bleach clean rinsing, it seems to take forever to rinse out in my Miele, and is very high sudsing. As of now the nearly full box and it's cousin, Tide Coldwater are in the discard pile awaiting delivery to mother's house. Yes, TWB cleans very well, but find like all Tide products it tends to not rinse well, and the scent just won't come out for several subsequent launderings.
Right now am using Tide "Professional Stain Remover" as a detergent in some loads, when not using Persil. It is "HE"/low foaming and though Tide Professional's customer service line tells one NOT to use the product as regular detergent, the MSDS says the product is simply Tide. Stuff is very concentrated and quite low sudsing,but give excellent results cleaning wise. Scent is "ok", but like all Tide products hangs around for awhile.
Soap In Laundry:
Will pretreat the odd stain or grimy collar with Fels soap (vintage stuff made by Purex), but overall find even with STPP softened water, soap has too many drawbacks for use in general laundry. It just does not rinse out well, and can cause tattle-tale grey build-up no matter what one does.
What one will do is swish a bar of Savon de Marseille or Fels soap around in a large Pyrex measuring cup of hot water, and then add to the wash through the dispenser drawer. Use this mainly for linens (Savon de Marsielle has a wonderful scent), and in the case of Fels Naptha Soap, for breaking down heavy scent residue on laundry and extra stain removal(Naptha is a great solvent based stain remover).
http://www.allbrands.com/products/abp09894-0711.html