I just got back from Batteries Plus. The guy was courteous,
and I bought some 9V batteries I needed. I reinstalled the
battery, and everything is now hunky-dorey. Knowing my luck,
the battery will fail tomorrow (though I doubt it).

Nice. Is it too late to have you measure the operating current
of the Dustbuster to satisify my curiosity?

It is. I've unbuttoned and rebuttoned it so many times I don't feel like
doing it again. But I suspect your 3A estimate is good. The unit uses sub-C
cells, and runs less than 20 minutes on high -- probably closer to 10.