The date is September 2 (if on the Sunday) or September 3 (presently booked Monday).
The One World ticket only allows one open leg, which we are using later in the itinerary. I can't imagine they'd let me cancel a leg -- even though there was a schedule change (of only about 45 minutes).

Jamienbaker, thanks. That gives me some hope, but OOOPS -- I see the Venice Film Festival is running at that time, which helps explain why hotel costs in Venice were so high! I've never dealt with BA before on FF tickets, but I've never liked anything about that airline, so perhaps I'm a little negative. Meanwhile I'm booking a cancelable hotel in London, just in case.