I recently found out you can get foaming soap refills as tablets. I hadn't previously found a way to refill hand soap pump style dispensers without more plastic. These are from Meliora.
I had this issue. Each refill tablet is a little different in thickness and each foaming foap dispenser has a slightly different nozzle diameter. Gotta find the magical combo that works perfectly for you. It's a little annoying but I found mine.