I'm wondering if this was one of those cases where the metro would
be quicker than a taxi, for at least part of the trip.

According to wmata.com, orange line to Vienna: 3:55 at Foggy Bottom,
4:09 at East Falls Church or 4:12 at West Falls.

I swear that I've sat withing walking distance of East Falls for longer
than 14 min on I-66 at evening rush.

Then a taxi from the station. Maybe Annandaler or another NoVA
person could suggest a reliable taxi company.