I'm running 3.12.0, to preface this.  It seems like the goblin eggs flush out before it's possible to encounter a valid mate.  Even after receiving the eggs then moving to a harpy square directly adjacent to it, the eggs flush out immediately.  Is this because my ass is truly that wrecked?  Or am I misunderstanding?

Ah, it seems the solution was more straightforward than I expected.  They can't flush out if you're plugged.