How about putting a very fine tulle on top of those blocks and/or doing free motion quilting on top of the tulle in the areas around the lettering using an invisible top thread? This should stabilize those blocks. The tulle will be barely visible but would protect the blocks.
Another thought if the fraying is just in the seams....use fabric glue along the seam to stabilize the frayed section and then do some couching with a coordinating cord or yarn to outline the blocks. It would cover the frayed section and also the area that is stiff from the fabric glue.