Federal Taxes: Can Both Parents Have FSA Accounts if They Have Joint, Equal Custody

I understand that the custodial parent for tax purposes is the one having the kids 183+ nights a year.

Here's my question: I have 5 kids and want 50/50 custody, and if my wife agrees, can she have 183 nights with 3 kids while I have 183 nights with the other 2 and still be able to have separate FSA accounts for childcare (and do things like claim head of household for that matter)?

It seems like a major tax benefit, and worth the extra weekend at mom and dad's house.

Federal Taxes: Can Both Parents Have FSA Accounts if They Have Joint, Equal Custody