Hi Antibodyverify,
I think the best way to go about this is to utilize the Customer:Job distiction in QuickBooks and Method. This way all of the universities would be the "main" customer, with each individual contact or department as a job. The setup would look like this UniversityName:Department. As you input a lead, you can associate the lead with the university and they will only sync over when you convert them.
I found this link that explain the Customer:job relationship more clearly
As this grows, you would likely have contacts for specific jobs, which Method can hold for you and and all of the billing would be separate for each job. You could also potentially customize Method and either run a report and build a screen to total up your sales for the entire university if you desired. There lots of possibilities with this setup.
Hope this helps,
- Adam