I'm pretty sure we're talking about going around South America if we're talking about the Panama Canal...
In the school district that I live in (and where my kids attend school), elementary school starts earliest and middle/high school both start at roughly the same time.
I've found that this works really well since my youngest wakes up and is ready to go earliest anyways, I don't have to adjust my schedule because they're out of the house before I have to get to work and I would need after school care regardless. My older kids can more or less fend for themselves before school so I don't need to worry about them while I get to work before they leave.
If elementary school started at 9 like high school and middle school I'd have to organize care for my youngest both before and after school since I'd be working at both times.
I agree with your conclusion but I think you have your numerator and denominator swapped.
$1,000,000,000 / 339,996,563 citizens = ~$2.94 / citizen