I work at a large private university and to my knowledge maintain the largest network of Linux/UNIX systems on campus.
I'd like to make an argument that going open source would save the university money and think through a gradual transition process to open source software (starting small, with something like replacing Endnote with Zotero, then MS Office with OpenOffice.org, and so on)
You're doing it wrong. Rather than gradually transition systems away from MSFT and Windows only solutions you need to give them the option to use both. As someone mentioned above it's not about cost but about what people know how to use and are more comfortable with.
What you haven't mentioned is which systems are you targeting? Universities have hundreds of departments and each have their own unique set of computational requirements.
For example, physicists, mathematicians and computer scientists, some chemists, structural biologists, and some electrical engineers can't live without Linux/UNIX systems. Why don't you offer to maintain systems for users like these (you'll need to hire other UNIX people, believe me this isn't a one person job). In fact this is my job and I have other helpers.
However, guys in business & finance, other arts & sciences dept. mechanical engineering and perhaps other engineering fields, and administrators need certain proprietary Windows apps.
I know some people at local universities who have switched machines that were just being used for checking email, web browsing, doing online research, or systems in the library for doing catalog lookups to NX thin clients that connect to a remote Linux desktop.
Another option is to provide a link on Windows desktops in computer labs or in areas where they need Windows apps (e.g. depts mentioned above) that starts Linux in VirtualBox (or your VM of choice) when the user clicks on them. I'm assuming all the users have a centralized storage area, you'll need to integrate the Linux and Windows home directories but it's doable.
The idea is that the curious people will hopefully start using Linux and you won't need to drive MSFT off campus because the users will do it for you.