Q. Is it ok to reimburse what she paid in 2022, because the payment goes toward the 2023 "allowable" amount?
A. Yes. In fact, you are required to do that so that the 529 reimbursements are made in the year expenses are incurred (actally paid). You are allowed to count first term 2023 expenses paid in 2022.
Q. Should we wait to reimburse her in January instead?
A. No. You are technically not allowed to reimburse yourself (or your student) in 2023 for money spent in 2022.
The fact that the total exceeds 2022 allowable doesn't matter, because (as you surmised) the payment goes toward the 2023 "allowable" amount.
