I don’t know that I can answer the substance of your question, which is the carryforward of any excess contribution.
The state website says the following about the deductibility of your rollover from another plan:
If your contributions were made by rolling over funds from another college savings program into Bright Start – the amount of the rollover that constituted investment in the prior qualified tuition program for federal income tax purposes (but not the earnings portion of the rollover) is eligible for the deduction limits discussed above. You should consult your tax or legal advisor about the availability of such deduction.
They also post an annual update of the previous year’s contributions in mid-February. And also the website says:
The person making the gift contribution may report it on their Illinois 1040 – Schedule M. Check with your tax professional for the proper tax reporting.
But nowhere do I see any chance of extending the excess contribution to future years for future tax deductions. Your CPA might have access to the Illinois tax department for more information. If you do find this is possible, please let me know. Great question!