I don't think that you will find an easy solution to this issue without aid from the librarians. There is only so much that you can do to fix a problem on a public machine without violating the terms of use. This is a good example of when Social Engineering is more valuable than technical know-how.
Tell the librarians that your security is at risk and so is their network since the version of Firefox is severely outdated (the current version is 1.5). Furthermore, tell them that it is very easy to update Firefox. All they have to do is log into the computer as a user that has priviledges to update the software (since I assume that they have the systems locked down), load Firefox, click Help, and select "Check for Updates". This will download and install the updates. All that they have to do is click a few buttons, and Firefox will update itself.
Unsolved 
