Traveller, I think that that with me, a regimen like you describe would dry my skin up and clear up the spots but then my skin would make more oil to compensate. Maybe try a thicker moisturiser once they're dry? I definitely don't have the answers though!! If someone discovers it let me know!
I was worried about that, , I've never risked the harshness of soap on my face before, but I use a normal moisturiser during the day so maybe that's helping. My skin doesn't feel dry but I guess time will tell if it's going to produce more oil to compensate for the soap.