It turns out that .net handles embedded resources a little differently than normal files; which is to be expected since they get bundled up in the dll. I was just expecting a second copy of my .js file to remain in its folder in addition to getting bundled, but it would seem that .net protects that file.
I was able to get my basic reference working correctly by navigating to the reporting pages which reference the embedded resource. Once the reporting system had correctly authenticated and downloaded the embedded .js file then my other page was able to use it until that authentication ran out. The long term fix of course it to add an embedded reference to the file on the new page as well.