I'm experimenting with a silicon bead on the top rim of the outer bowl to keep them from slipping during use...I'll let you know...
How about a large O-ring?
Get an O-ring that will sit around the bottom lip of the lathering bowl, tight up against the body of the bowl to keep it in place, and it will then act as a buffer between it, and the scuttle portion.
Check out McMaster for all shapes and sizes of O-rings. They sell little tiny ones, or big ones that would certainly be large enough to fit your lather bowl.