Do you have any links to recipes for homemade laundry soap that you like? Or suggestions on what makes the best homemade laundry detergent?
Soap based? Of course you should use the most grease-cutting soap you can, i.e. the highest feasible proportion of coconut, palm kernel, or babassu -- 100% would be best -- and no superfat, but also as close as feasible to 0 lye excess. And the product should be mostly soap. Extra alkali should be no more than 20% of the total weight.
As to the added alkali, lye is no good, and while washing soda and borax are not bad, you can do a lot better, particularly with sodium silicate. (Sodium silicate provided the "-sil" in Persil, and the rinse in Rinso.) I don't know what the optimum Na2O:SiO2 (alkalinity) of sodium silicate is, but it's in the middle somewhere. And with silicate you need even less than with carbonate or borate.
Phosphates are good too. Not trisodium phosphate -- too alkaline -- but lower alkalinity phosphates: tetrasodium pyrophosphate (OK as among alkali mentioned above), [penta]sodium tripolyphosphate (better), or sodium hexametaphosphate (soluble sodium metaphosphate glass). The latter two are of low enough alkalinity that you can use more than the 20% limit I stated above. Indeed, if the water is very hard, adding a phosphate builder (along with a pinch of silicate) is the only feasible way to go if soap is your only surfactant, and just increase the total amount you use per load. Deselex + borax can be used as a phosphate replacement.
Until fairly recently, the state of the art for soap-based laundry detergents was a silicate-built soap powder with also a small addition of a nonionic surfactant of the type used in Lestoil, Shaklee Basic H, or spermicide, as well as the lowest-sudsing soapless detergents -- ethoxylated alcohols or alkylphenols. The nonionic surfactant along with the silicate was to disperse lime soaps, preventing tattletale grey from use in hard water. However, since then there have been developed certain specialized surfactants -- one class I remember was of disulfonates -- that actually work together with soap in hard water to clean, and don't just deal with a byproduct of the soap.
But don't think you can get by with just tablespoonsful per machine load as suggested by some of the home recipes that are widely posted. Some of those recipes are so alkali-heavy that it's possible you may
have to keep the amount you use per load that low just to minimize the amount of damage it does to fabrics, but it's doing hardly any cleaning then. Unfortunately if you're using soap, you need to use enough to get the water good & sudsy, and forget about using it in HE machines. The nonionic surfactants mentioned above, along with alkali, will reduce the suds a little, but maybe not enough to make HE washing with soap feasible.