I think, not necessarily ferrite, some soft magnetic alloy of about 1/16" thick will do. For the experiments it's OK to make it manually, with pliers. Besides, I feel the U must be oriented along the strings, not perpendicular, so, we can easily afford extra 1/8" of space.It's an interesting idea, but I think you'll find that trying to make an E-core that will fit into that small a space will be terrifically challenging, if not altogether impossible.
McSeem