I must be searching with the wrong terms, because this seems like an issue everyone would be having that uses eclipse web projects. Maybe no one does, but if two projects import different versions of a library (i.e. slf4j), they both get included in the war by eclipse.
See https://github.com/thatguy1177/gradleWtpExample for an example project. You just need to import the project as a gradle project, and when you build a WAR using export, or look at the wtp tmp directory, you will see multiple versions of the same libraries.
Anyone have any ideas where I should even start, the gradle plugin maybe? Not sure.