I've spoken to Apple about this and it confirmed the impression I got from elsewhere: there is no fix, because this change is a consequence of some of the other changes they made to AirDrop.
I used their "feedback" system to say that this was a regression that slowed my workflow but brought me no benefit, and requested that they offer the option of choosing what app should receive a file even if that meant that people selecting that option had to give up something else. Doubt they'll take any notice, but I figure that if nobody complains they'll think everyone is happy, so what the hell.