Given the results in TurboTax, your MAGI for the purpose apparently exceeds that amount above which no deduction is permitted for a traditional IRA contribution. There is nothing that can be done about that unless you have other above-the-line deductions that can reduce AGI.
Note that the $4,500 is not entirely lost to taxes, it just means that you are paying taxes on this $13,000 now instead of later.
