I barely press the label sheet on the fabric. It sticks well.
I use a long stitch with a washaway stabilizer on the back.
Some sewists use a zigzag. Your choice.
Depending you your design detail, I cut apart the design like a puzzle if it is a simple design and stitch around the edge, not catching the paper. Detail designs do not show up well on fleece.
If you are outling then cutting out the design so the back fleece color shows through, I would use the school mascot and not an super detailed logo. If you are doing simple letters for the university, then stitching around the label paper would work best.
Perhaps we can help more if you could give more information.
Size of your design
Copy of the design
What exactly are you doing with the design
Are you only outlining or appliqueing?
Best wishes on your project.
D in Tx