Are you going to work till the day of birth?

Don't you need to use some vacation for the 2-3 weeks before your due date? Both of my babies came to the world 2 weeks before their due dates.
I suggest that you take the maternity leave and all remaining vacations before you take the unpaid leave. According to Family Leave Act, you can stay home for up to 12 weeks, including all maternity leave and available vacations. It just seem odd that anyone would take unpaid leave before the accumulated vacations are used up.
If your boss's concern is if he can hire another team member, why don't you take 4-5 months off? Once you have your baby in hand, you will want to stay home as long as you can.