When I look on NHGIS, I find that the tables in 2000 Summary File 3 are limited to ages 16-19 and 18-34, just as you found. But I also see a few other relevant tables from the 2000 EEO (Equal Employment Opportunity) special tabulation…
It looks like the first two tables give counts for the “labor force” and the 2nd two give counts for “workers,” which suggests to me that you could divide the latter by the former to get employment rates. Unfortunately, these are broken down by race and ethnicity and by many occupations, so I think you’d have to select get all of these counts and sum up across all those categories to get a population total. And you’d probably also have to select just a few occupation categories at a time to avoid going over the NHGIS limit on request sizes. This would not be easy!
In short, it seems possible but quite difficult using data from NHGIS. I’m afraid I don’t know of other options. Using microdata from IPUMS USA could allow you generate your own cross-tabulations, but most counties are not identifiable in public use microdata, so I suspect that wouldn’t work for you either.