Well, I tried it tonight. I used Dr. Bronner's Castile Liquid Soap in the dishwasher. Last night I use Dr. Bronner's Sal Suds with great results.
I was too lazy to make up the recipe(see original post), so I placed a few squirts of my 50/50 Dr. Bronner's Castile soap mixture which I use for the bathroom in the dishwasher's detergent dispenser. I refilled the rinse dispenser with vinegar, and the dishes came out fairly clean. I had more plastics than glass this time, but the few glasses that were washed came out clean without any film, and no spots. I did find one glass bowl in the back which still had a bit of oatmeal film. I plan to add more castile soap(70/30) to the mix in order to see if this improves the cleaning power. It still did a good job.
I just got an awesome new dishwasher, so that maybe a contributing factor to the great results here. It's not an expensive one, but it's a nice new Kenmore with lots of fancy jets. I run my dishes on the ecocycle, so it's less water than the normal or heavy wash cycle, and still they look great.
I think what I'll do is use the Sal Suds for the really greasy jobs, and continue to use the castile soap for everyday dishes. I'll keep using these products because of their cost effectiveness and eco-friendliness, not to mention other factors which made me feel good about this product. Dr. Bronner's is certified organic and fair trade, American made, and is still a family owned business that has not sold out to big corporations. A company with integrity, a rare gem, and I'm happy to help them with my purchases of their quality products.
Note: Don't try regular liquid soap, it will bubble too much and possibly break your dishwasher.