...or provide a way for me to customise the script so that I can do this. Or something similar.
On the Semigroups and Digraphs package websites, we like to include an up-to-date copy of the CHANGELOG.md file; these are provided https://digraphs.github.io/Digraphs/CHANGELOG.html and https://semigroups.github.io/Semigroups/CHANGELOG.html, respectively.
When we used to run ReleaseTools locally, we had our own release script that we ran before running ReleaseTools, which (amongst other things) copied CHANGELOG.md to the gh-pages subdirectory. But now that we want to do the release, or at least part of it, in GitHub Actions, then I think we need another solution.