Your math is off. You're starting with the number that already excludes things like non-custodial parents and runaways, wandered from care and so on.
The 200-400 number represents the final total of lost or stranger abducted children children, not young adults.
And that number is pretty good for a population of 350 million! It's also 300 children who have been kidnapped and likely face an unpleasant and grim fate.
I would happily charge everyone in the country $0.05/child a year in additional funding to lower that number.
We can keep it budget neutral by canceling a few fighter jets.
Keeping people alive is an easy sell for tax dollars for me, particularly when it's an issue that would actually benefit from coordinated research and expertise. It being children speaks more to the priorities of humans than strict economic accounting, which is why I padded my figure by 80%.
And that's before we even get to a progressive tax system shifting most of the cost towards people who can afford $30-$250 a year in additional taxes.