Ammonium hydroxide would work but you'd end up with the ammonium salt of the oil instead of the sodium salt. The ammonium ion would then degenerate to ammonia at anything other than acidic pHs and very quickly at alkaline pH. So if you want to work at pH 13, your ammonium salts would decompose to give ammonia and a salt of whatever simple metal ions you have in your earth, mostly calcium I guess. Calcium salts of soap are notoriously insoluble in water and are responsible for the scum you get when using soap in hard water areas.In other words, you could saponify the oil with ammonium hydroxide but I shouldn't think it would be good for much after that.
There are special organic derivatives of ammonium salts that organic chemists use to make detergent molecules but they're made by a different process. I'm not entirely sure of the details but I expect it involves ion exchange between the sodium/soap salt and the organic-ammonium salt. I also suspect that sourcing your organic ammonium derivative would be no cheaper than sourcing the detergent in the first place.
As for the glycerine content, you'd have to talk to the suppliers about that.