@xmasbaby0 - I appreciate your quick reply and discussion. I think my error is assuming that "custodial" and "noncustodial" terms apply to unmarried parents living together based on their AGIs. If the child lived with both parents all year, this is not what is meant by a tie-breaker test.
I found an example in pub501 that seems to match what you are saying - that only one parent gets to claim all the benefits.
"Example 8—unmarried parents.
You, your 5-year-old son, and your son's father lived together in the United States all year. You and your son's father aren't married. Your son is a qualifying child of both you and his father because he meets the relationship, age, residency, support, and joint return tests for both you and his father. Your AGI is $12,000 and your son's father's AGI is $14,000. Your son's father agrees to let you claim the child as a qualifying child. This means you can claim him as a qualifying child for the refundable child tax credit, head of household filing status, credit for child and dependent care expenses, exclusion for dependent care benefits, and the earned income credit, if you qualify for each of those tax benefits (and if your son's father doesn't claim your son as a qualifying child for any of those tax benefits)."
