  While equality of skew Schur functions is well understood, the problem of
determining when two skew Schur $Q$ functions are equal is still largely open.
It has been studied in the case of ribbon shapes in 2008 by Barekat and van
Willigenburg, and this paper approaches the problem for near-ribbon shapes,
formed by adding one box to a ribbon skew shape. We particularly consider
frayed ribbons, that is, the near-ribbons whose shifted skew shape is not an
ordinary skew shape. We conjecture, with evidence, that all Schur $Q$ functions
of frayed ribbon shape are distinct up to antipodal reflection. We prove this
conjecture for several infinite families of frayed ribbons, using a new
approach via the "lattice walks" version of the shifted Littlewood-Richardson
rule discovered in 2018 by Gillespie, Levinson, and Purbhoo.
