After a lot of research and having talked to one of the Lombok developers, it turns out that because javac does class loading based on hashCode(), the order of annotation processors running in this scenario is essentially random, and what’s worse, random between multiple runs. There currently does not seem to be a solution to this issue.
I went with the lombok-maven plugin and delomboking the whole thing, which isn’t perfect and somewhat hacky, but at least produces a working result. In hopes that it may aid future googlers coming here, I commited the working version to the repo.