I saw your post and wanted to know if you have had any luck dispensing the soap. I have been in touch with the sullivan pump company (they make fuel pumps for the RC hobby industry. They recommended the S752 fuel pump, though they did caution some uncertainty with laundry detergents with bleach.
Please let me know. I plan to make the same circuit, but doubling it to also dispense fabric softener.
I know the pump works even with thick fluid (I tried with my costco laundry detergent. It takes about 20 seconds to get to the middle line at 12V
If you have a sketch, I could use it to save me a lot of trial and error programming.