You can make an estimated payment now (for Jan-Aug), although it will be a bit late since it was due Sept 15, and another payment by Jan 15. Then, just file and wait for the penalty assessment, if it comes. You can then apply for a waiver or abatement for cause. Save copies of your correspondence with the university.
https://www.irs.gov/payments/penalty-relief-due-to-first-time-abate-or-other-administrative-waiver
I would not let turbotax or any tax payment include a calculation for an estimated penalty. It's easier to ask for the abatement when you get a bill, instead of paying the penalty up front and then asking for an abatement.
Depending on how you are paid and who pays your stipend, they might be making the right decision (at the wrong time), but you don't give enough details to evaluate that.
