FWIW, we found that we can dilute Dr. Brommer's soap with water and it works really well in those same foaming soap dispensers (and it foams!). Pure organic saponified oils for washing my hands... for the win.
I just want to plug another awesome use for Dr. Bronner's--as a replacement for spray cleaner. We used to get the windex or 409 or whatever it is, the stuff you'd spray on counters and wipe up with a paper towel.
No more, I now dilute a little Bronner's in an old spray bottle with a lot of water, spray it on, wipe up my kitchen debris, stuff smells great, cleans up the counters a treat, and is insanely cheap for the value.
Are you just re-purposing standard off the shelf foaming soap dispensers or did you buy something in particular (e.g. can I reuse a Method foaming dispenser)?
I have found that my homemade water-soap mixtures will eventually cause the foam soap dispenser to jam up and stop working. Adding in a small amount of glycerin seems to help keep the dispenser lubricated.