If you want to try the soap solution there are two methods I've used before. I put one squirt of liquid soap in a small spray bottle like from a dollar store and then fill with water and just spray the inside of the belt. Also the bar type hand soap that you get from a hotel works good too, just rub it onto the belt then start the engine to spread it where you can't reach.
I know you stated that the belts were tight, but are they too tight? Check for play also. Also check and make sure that the belt didn't jump a rib on a pulley and is running true. Have seen this happen after washing the engine area, a small pebble can get in a pulley causing it to jump over.
Another thought, did you use a chemical to clean with. Some chemicals leave residue and can take some time to wear off.