Maybe they could do something with the githyanki egg too (if you take it) because it would be hilarious, yet heartwarming seeing SH raise a gith child, considering how she was before lol
You can convince the caretaker of the Gith egg to hand it over to you for a better future (the Creche were planning to eliminate it, but he was the last of his clutch so he had a soft spot for latecomers). He'll ask you what your plans with it are, and if you tell him you'll raise it as your own flesh and blood, Shadowheart will approve.
Pretty much settles that she'd be completely fine with that! After all, if she approves of you doing that, and she becomes your spouse, then she'll automatically be part of that too.