I'm a bit confused by what you mean by only accepting monster babies, I thought you can't get pregnant with anything but the creatures you listed? The baby was a deepone because I was able to use it to start new game + with the fishy option. Do they change over time after birth?
Lona can give birth to Orkin and Goblin babies, these can be sold to Elise.
If you want to reborn as an abomination, you need to sell 2 abomination babies that Lona gave birth to Elise using the "Sell Child" option, NOT barter. For a mixed race between Abomination + Moot, you need to sell 4 instead.
You can abandon human, moot, and deepone babies at the church and still preserve the option to reborn (this is so the baby doesn't drain your resources).