So it has been a long wait, but it has finally happened. This is how the official-looking letter I received last week Friday starts:
"Hierbij treft u aan een bevestiging van de verkrijging van het Nederlanderschap door optie."
Meaning that I am now officially a Dutch person as well as an American, having acquired dual nationality. Now I can be treated as a full-fledged European, able to work and live and play in any of the EU countries.
Something to celebrate tomorrow evening with a fun dinner with the whole family.