Not to try to discourage your experimentation--I thoroughly endorse mad science in all its many forms
--I don't think you'll have great success with other household-safe bases. It takes heat and a pretty strong base to break up a fat into its constituent fatty acids and glycerol backbone and then react to form the salt we all know and love as soap. If you managed to get your hands on the pure fatty acids you might be able to react them--probably under pressure and heat--with weaker bases like baking soda. But a catalyst-free reaction with unbroken fat molecules isn't likely to go so well.
I wouldn't use ammonia as a base if it were me, certainly not for something I planned to use on my skin. Ammonia salts are toxic as all get out. You might be able to make something that would work as a general-purpose cleaner, but please don't use anything made with ammonia for bathing!
I'm interested to see how your experiments turn out. Let us know what your results are and
ONWARDS! FOR SCIENCE! 
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