Babel not transpiling chunk-vendors for IE11, in Vue-CLI project
The answer seems to be, not so much "make sure all dependencies are transpiled" (which apparently can cause a lot of problems), but "make sure the specific dependencies which are causing issues are transpiled".
You can do this by adding a line to vue.config.js:
transpileDependencies: ['/node_modules/myproblematicmodule/']