Self-dual Specht-filtered modules are trivial source modules

Let $k$ be a field of characteristic $p$, let $\Sigma_d$ be the symmetric group, and consider indecomposable self-dual $k\Sigma_d$-modules with Specht filtrations. A module is trivial source if its source is the trivial module for its vertex.

Trivial-source conjecture. Indecomposable, self-dual $k\Sigma_d$-modules with Specht filtrations are trivial source modules. This is a proposed weaker replacement for the earlier conjecture identifying these modules with signed Young modules. The preceding discussion notes that signed Young modules are trivial source, while examples show that the class of self-dual Specht-filtered modules is larger than the signed Young modules; the conjecture remains unresolved in the supplied text.