Could this have come out of the egg sac? I just looked through the guide and I saw several images of these feeding on wrapped prey of spiders, but I didn't see anything about them being associated with egg sacs.

I think I still have the specimen, if it would be of interest to anyone (or if there are other shots I could add that would help ID it further).

Photos showing the entire wing and a dorsal view of the head would help ID this (an expert could probably get it to genus from this image, but I can't). Known larvae in this family are generally saprophagous, so if the egg mass was rotting that could have been where this developed, but I don't think direct parasitism is known for milichiids. If you want to pursue this, Irina Brake at the NHM in London is probably the person to talk to.

Perhaps it's more likely that this fly was associated with the moldy moth pupa, of unknown origin, that was in the jar with the egg sac. I don't know what possessed me to put those two things in the same jar; I guess I figured that if spiderlings and a moth emerged, it would be clear which came from what. Now that I'm getting all these interesting parasitoids etc., I'll be sure to be more careful about only having one item per container.