I like (real) Aleppo soap, which is 65% olive and 35% laurel oil. very gentle on the skin and desinfecting as well. Recommended for problem skin.
Made in Syria, 1000 yrs tradition.
www.paindalep.com
Have you tried the Oil Cleansing Method? It is very gentle, and removes oil and grime very well.
1. Mix equal parts olive oil and castor oil. More olive oil = more moisturizing, less olive ... less moisturizing. This way you can adjust it for your face.
2. Rub it on your face. Unlike with water, the oils on your face and in your pores will mix into the mixture.
3. Place a hot towel on your face just like with beard prep so your face can soak up some moisture.
4. Give a quick rinse, and if you need some extra moisturizer, you can apply a very small amount of olive to your face, or use whatever else you wish.
I found Ugarit, a soap company in Aleppo, Syria. However, neither site lists any buying information.