I highly recommend any products from LUSH. I used a shampoo bar while traveling in Africa for the same reasons you mentioned, and I was such a fan now it's the only thing I use.
They don't have a total all in one product, but they do have a combined shampoo/conditioner bar:
http://www.lushusa.com/hair/shampoo-bars/godiva/02392.htmlOne bar usually lasts me at least 2-3 months (of every other day use). If you lightly dry it off with your towel and put it in it's little tin after using it should work great for you.
For face/body I would go with a Dr. Bronner bar soap:
https://shop.drbronner.com/castile-bar-soapOther things I used in Africa, trying to avoid all liquids: face wipes (favorite is Trader Joes tea tree oil wipes, excellent for getting off grime at the end of the day), toothpaste tabs (from Amazon--they actually produce amazing lather), DEET wipes (best thing I brought-one wipe covers the entire body, and you will not get bitten).
I don't know if you are a male or a female, but there is an excellent website (
http://herpackinglist.com/) that is geared towards helping women pack smartly and efficiently for backpacking trips, has a ton of product reviews, etc. I scoured it for weeks and it was the backbone for all the decisions I made for Africa. They are also very cost-conscious in any recommendation. I think it would be helpful for anyone, not just women.
Sounds like a great trip, have fun!