As luck would have it, I just soloed this quest this morning (it was the next one on my todo list). For lack of any other plan, I went with the old "lead her to the cliff above the shrine" trick. It worked like a charm. I didn't turn around to see how far up the corridor she followed me, but once I dropped off the cliff, I was free to head back into her cave and take out the eggs (and get the chest). Had a slight scare, as one of her black widow friends returned just as I was FOing, so I had to stop to kill it. No one else came back and I finished out with no problem.
Maybe I just got lucky. But it seems to me the cliff trick still works to some extent.