Most of the kids in NY state are living under the care and support of their parents and aren't working, therefore they shouldn't even be a factor in population/labor force participation metric.
Additionally, many of the old people who aren't working shouldn't be factored in either because they are receiving quite high pensions to live from, as well as social security.
When you factor this in, my initial ratios still stand. Out of the 325m people living in the USA, 45% are working (145m). When subtracting the 30% of Americans who are retired or under the care of parents, you are removing 100m people.
Therefore, as you say, the "prime age" labor force participation rate is 65% (145m/225m).
Applying this ratio to my original numbers, 45.5 million people are laborers in the Northeast. The other 25m either used to be laborers or are protected financially by laborers.
We cannot possibly say that an area like Amarillo TX, with just 100,000 laborers, is indicative of some nationally sustainable trend where cost of living is cheap and wages are still high.
This denies the existence of an extremely large block of humans, who are struggling despite earning decent money.