Re: Should I err on the side of patience?
EDIT - started writing before your post appeared Bison, sorry for covering some of the same ground!
The timing of this doesn't quite work, there is something else going on.
Multiple eggs may indicate laying workers, but not always.
At this stage, my advise would be give them a frame containing eggs from your other hive, then a week later have a look and see what is happening to the eggs that have been laid multiple to a cell, ie, are they developing normally into worker larvae, are they drone larvae in worker cells, or are they gone altogether. Also check the frame of young larvae you added to see if there are queen cells. Then post up here what you found & we will have something to go on.
44 years, been commercial, outfits up to 4000 hives, now 120 hives and 200 nucs as a hobby, selling bees. T (mostly).