You may not need rings being you used water. Years ago when lapping was more common it was so problematic that a special detergent was developed to use in conjunction with a scrub brush to clean the parts of residue. Today a car wash would be handy.
It was found that when using solvents of a petroleum nature the compound was not being removed well. I've personally seen it happen in 2 automobiles and several lawn mowers. One of the autos was a pickup I bought pre owned at a ford dealer. It wore the rings and ring grooves so bad the rings actually broke. Top ring in several pieces. That's when I discovered what that strange whistle sound was. I didn't know rings could whistle but they can. The tune is just mono tone and boring.
Here is hoping your cleaner overhaul will make a good engine.