A week later I checked, to find developing brood, with multiple eggs in cells. I assume that I have a couple laying workers, and a lost queen.
Don't assume multiple eggs in a cell means a laying worker. It is quite common for a young queen to lay 2-3 eggs in a cell until she "settles" down.
Now if your finding 5+ eggs in cells and no pattern to the laying, then that would be more of a sign of a laying worker.
I just went through a similar ordeal this weekend. A few weeks ago I had a queen introduction into a split fail, and they built some queen cells. I was in the process of grafting some more queens so I just left them alone, hoping to replace the cells with one of my grafting, before they hatched. Well needless to say when I went to install my cell, I found a virgin queen running around and a couple of other queen cells had hatched. I figured there was no way I would find all the virgins, so I did not put in my cell. I would let them duke it out and settle on a queen before I tried re-queening again. On a subsequent inspection, the original virgin was gone and I saw another. A week later I saw some eggs, a little sporatic, but nothing I hadn't seen before. On the last inspection, all the eggs were capped drones, and no queen to be found.
Since it is very hard to get rid of a laying worker and re-introduce a queen, I just shook all the bees out and took the hive away. The bees immediately found the hive next to them (hive they were split from).
The laying worker either won't find the hive, or if she does, will be killed by the queenright hive.