I don't know what form 8959 has to do with you. The 8959 is used to report "additional Medicare tax" which is Medicare tax on incomes over $250,000 (married filing joint). Is the university paying you that much? (If they are, I want your job)
As for the 843, you are in luck, because the instructions say "A refund to an employee of excess social security, Medicare, or RRTA tax withheld by any one employer, but only if your employer will not adjust the overcollection." See 843 Instructions, page 1.
It is good that the university is co-operating. See the instructions under the subheading "Refund of excess social security, Medicare, or RRTA tax." (page 4)
"If you are claiming a refund of excess social security, Medicare, or RRTA tax withheld by one employer, you must, if possible, attach a statement from the employer. The statement should indicate the following.
• The amount, if any, the employer has repaid or reimbursed you for excess taxes withheld.
• The amount, if any, of credit or refund claimed by the employer or authorized by you to be claimed by the employer. The employer should include in the statement the fact that it is made in support of your claim for refund of employee tax paid by the employer to the IRS."
So read the instructions carefully. Also make clear in your statement the way the SS tax has been treated versus the Medicare (one partially paid back, the other not). Also, be sure to note how much the uni repaid, and add your W-2.
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