Basil - yours was a valid theory and I worked on it earlier today, defeating first the Dregs, then moving to the Flotsam, in the order the quest was presented, but the Flotsam weren't counting towards the quests.
Logged out around 3:30 central time. Logged back in at approximately 9:40 central time and had a short test update.
I'm happy to report that the staff quest is now working again.
Woo-hoo!
ETA: I have not checked yet to see if the Murky Hollow dig spots are now functioning. Will leave that to someone else as I have major staff envy and want that sucker in the worst way.