IV Approach your target(s): Do not attack your target(s) - go to them and explain what you want to do and why.  Be nice and courteous; they may have already considered doing what you're asking but not had the resources, information or support to change paper purchasing policies.  Remember, at UVa and Rutgers the buyers wanted to help with the students' campaigns, and they did!  Also, approach your target(s) at the appropriate time.  You should have your initial research and information gathering finished.
Before you talk with your target(s), know the products and prices that your university purchases.  Be able to offer competitive prices or have a feasible economical solution.  For instance, you might be able to purchase 100% recycled toilet paper that is cheaper than toilet paper currently being used and that could off-set having to spend more on copier/printer paper.  You might want to come up with a paper reduction solution that would allow spending more on TF paper.

A. Possibility of revising plan of action:
There is a possibility that after you approach your target(s) that you will have to change your plan of action.  You might be lucky and find that your purchasing department just needs to be connected with a distributor or you may run into a brick wall where no one wants to help you.  Kevin Lyons at Rutgers initiated everything and determined the plan of action for that university.  At UVa, Althea White does a good job finding post-consumer recycled paper and works with other schools in order to offer a larger market to potential distributors, but lets the student groups work with getting the individual departments to switch and campaign strategies.
Be flexible - even though you have come up with a beautiful plan of action, parts of it may not be necessary while other parts might have to be intensified if you aren't getting any positive responses from your target(s).