Thanks for the advice. I had initially checked my entry/ departure, and it showed "not available", which got me worried and prompted the query to FT. But rechecking it today, it does show my departure date correctly, although it states location as "not available" (it was LAX), and same remark on a couple of other previous departures (and I entered US without issue after those -- those weren't paper I94 journeys).

I'm going to keep my BP in my travel bag, but I'm thinking (?hoping) that I now don't need to send in my I94 as a back-up...

tb