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So, I ran experiments to test the rejecting egg part for swapping between gendered and genderless/fixed gender mons. You can see them in pic related. I took a Marill and an Alakazam and bred 10 eggs with each of them. Noted down the IV inheritance, gender, nature and ability. The other parent was a Chinese 6IV Ditto. The cells in pink are inherited from the mom, blue from dad, green are random and orange were random incertainties that got taken care of by comparing Marill and Alakazam results.
Then, I did the same for Miltank and Lilligant, which can only be female. The catch is, before accepting an egg from the day care girl, I rejected one. I repeated this pattern 10 times, for an alternating sequence of rejecting and accepting (20 eggs total). The results matched the Marill and Alakazam results EXACTLY for IVs and nature.
Ability was also exactly the same for Miltank, who had the slot 2 ability just like Marill and Alakazam. Lilligant, however, had the slot 1 ability, which generated a completely different ability spread. Clearly, the numbers used for randomly determining the ability were the same, otherwise we wouldn't get 10 eggs to match IVs perfectly. So it seems there is a more intricate mechanism at play for ability inheritance, that takes into account the parent's ability.
Unfortunately, I have to go right now so I can't run more experiments. I will come back in a few hours to do more, though, so keep the thread alive.