I think I would have to distribute both the original source and the LaTeX source and an explanation of what happened.
You forgot one of the most important parts: The perl script. I'd suggest distributing the original, the script, and a diff.
It's true that the GPL wording implies that there is a single "preferred form",
Yep. The GPL was designed for compiled programs, and it shows in several places.
but in this case there seem to be several such forms, and it makes more sense to understand the GPL as referring to all of them rather than forcing a choice between them.
Agreed. I'd only consider dropping the original unidirectional dictionary as source if there were extremely extensive changes (such that trying to regenerate the final work using the perl script would clearly not be preferred)