As you discovered, Amtrak, unfortunately, is not much of an option. Morning departure only, arriving San Jose about 8pm or so (theoretically, if it's not late -- there's a reason that train is nicknamed the Starlate).
If you or anyone else is ever in this situation again in San Francisco, you can take Caltrain to Millbrae and catch BART from there to the airport. Somebody actually planned a convenient transit connection in this country!
Enjoyed the report!