You can find washing soda is small markets sometimes, we have it in our local camping-store type place. It is a very old product so it just depends on who is ordering for the store. Here in WA you can get it at Winco.
I used Zote very successfully in place of Fels Naptha.
I've heard the suggestion of whitening by using bleach, adding it to the batch of (liquid) laundry soap. To me, when I heard that, I thought, well why not just add bleach to my machine the old-fahioned way? So that is what we do when we need to whiten socks or sheets or whatever that are getting gray.
I've also heard of adding baking soda or vinegar to the recipe with good results. Baking soda to freshen odors of course and vinegar is supposed to be good in the rinsing.
In the recipes I've seen the amounts varied and looked kind of non scientific. The one with baking soda said to just add a cup of baking soda and this was a recipe that called for a cup of borax, cup of arm and hammer, one bar of soap and five gallons of water.
I would think adding baking soda would be easy to do with the dry recipe as well.
I've also heard of using equal parts baking soda and borax for dishwasher detergent. It worked okay when we tried it but I like using the liquid laundry soap better.