Here is what I think you are saying.
You took a distribution in 2018 that paid for classes that started in 2019.
That is 2018 transactions and has nothing to do with 2019. You had to deal with that distribution on your 2018 1099-Q.The tuition expense you paid for the 2019 classes is gone for 2019.
Just because neither parent can claim the student does not mean she can claim herself. She can only claim herself, and the full credit if available, if she supplied more than have her own support.
So, if she is able to claim herself, she simply enters the 1098-T. She does not have to report the excess 4,000 from 2018, in fact she can't. That should have been dealt with on the 2018 tax return of the recipient listed on the 1099-Q.
The 1098-T lists "What was paid in 2019" so whatever you paid in 2018, even if it was for 2019 classes, won't be on the 1098-T.
So in conclusion, if the student can claim herself, she can enter the 1098-T and apply for an education credit. there is no 1099-Q for her to deal with.
IRS Pub 970
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