I finally got around to testing Scala.js with this RC. I managed to make it work with the following build-time amendment:
set scalalibInternal.v2_13/Compile/sources ~= { val excludes = Set("Any.scala", "AnyRef.scala", "Nothing.scala", "Null.scala", "Singleton.scala"); prev => prev.filterNot(f => f.getParentFile.getName == "scala" && excludes.contains(f.getName)) }