The way I always figured it happening was like this.
Anti-Spirals would implant a new messenger into visible planetary populous at random. Select a randomly developing fetus, or some such. When that 'carrier' expired, they would implant a new one. The Anti-Spiral actually says about this much himself in the last episode.
'Your being the daughter of a Spiral Warrior, and falling in love with a Spiral Warrior were all coincidence'
Here's were the speculation begins in earnest. The only new births that the Anti Spirals could detect on earth were Genome's daughters (since the rest of the population was underground, and harder to detect). So they were pretty much pre-determined to be Anti-Spiral messengers. Weather or not Genome knew this for sure, it stands to reason he suspected it to be the case. Even if that is the real reason for him throwing out his daughters I still think that some minor genetic tinkering on Papa's part is the best explanation for her eye's.