If I'm reading this correctly, it seems that for each analysis, all branches were tested for signatures of selection (with the exception of SLAC which assumes selection is constant across the entire tree)? Although RELAX and aBSREL can be used to test each branch, each are significantly more powerful when used in a hypothesis-testing framework, assigning a subset of branches to the "background" (control) and the remainder to the "foreground" (treatment), and estimating parameters within each test-set. The per-branch tests are generally considered to be most useful in exploratory use-cases.
I think this use-case scenario is ideally suited to the hypothesis testing framework of these two models. Specifically, to test the hypothesis that selection on cocoonases intensified (or was relaxed) in H. aoede as compared to the rest of the Heliconius butterflies, you could treat H. aoede as the foreground, and the rest of Heliconius as the background for both RELAX and aBSREL. It's unclear whether cocoonases in Eueides or other species within Heliconiini should be experiencing the same/similar selection regime as in H. aoede, so I would suggest excluding those species from this specific analysis.