Last night before I went to bed, I checked on the soap, which had solidified into a rubbery circle in the pan. I added water and stirred. Then stirred some more. Finally it obtained a slime-like consistency. After that, I decided to leave it alone and go to sleep.
This morning, I still had a pot of thick slime, so I added three more cups of water and heated it up again.
After allowing it to sit for a few hours post boiling, it was at a honey-like consistency, to put it nicely. Otherwise, it was kind of like a big pot of snot, thanks to the color. It seemed like I had to keep stirring and re-stirring to keep it at a normal consistency, but when left alone it would separate from the water and return to a thick chunk of slime.
Ready to throw in the towel, I tested it out with a pump and it didn't seem to clog the pump at all even though it was slightly clumpy. Basically I gave up trying to get a perfect consistency like store-bought liquid hand soaps. I didn't seem possible, at least with this brand of soap that I found at Big Lots. It was made from 100% vegetable oils & no animal fat. Different soaps will do different things though, so if you try this you may very well have different results. A clear glycerine soap might work at lot better? I added a little colorant so that it didn't look so much like, ugh, well... snot. Even though it's not the most attractive liquid soap, it does seem to work okay but I don't think my soap experiments have come to an end just yet.