I figured out why the web app I was trying to build before broken when I used the exported build script. Turns out that you need to run a setup script to get your environment "just right" before running the build.
This setup script can be found in any weblogic domain. Of course, this wasn't documented anywhere, but I did find a link in BEA's support database, so partial apologies back to BEA.
Now, all I need to do is figure out exactly which part of that 314-line abomination (most of which simply sets up the system classpath, which is something that is extremely bad to do on a build script) is actually needed to get the project to build without the ExceptionInInitializorError it gives.