Ok so we introduced the chicks last night like I described. Went fine at night, and they were fine when I checked on them first thing in the morning. Seeing their success, Dad gave Cloud two more in the morning so she had four. Not a good idea.
Once the chicks started waking up, Cloud decided to reject her four.

She chased them out of her cage and wouldn't let them come near her. Apparently the chicks can get through the dog crate

so note to anyone who might use this method: attach hardware cloth to do the dog crate or SOMETHING to keep the chicks in. Though in our case it was probably good since the chicks were able to escape and thus were uninjured. They were running around the coop though and going between the cages and freaking out.
Luckily Ash (she and her chicks are uncaged and have free roam of the coop) and Nutmeg were dutifully collecting any lost stragglers, though Ash didn't want the black chicks at all and she'd nip at them for some reason. Nutmeg is doing great with her chicks and has no color preference. She immediately switched to mommy mode and is making cute little mommy chicken sounds so we gave her more until she had 12, and we let Ash keep the ones that had run away from Cloud so she has 12 as well. The last 6 chicks are in the brooder inside since we don't have anywhere else to put them.
So it worked!!!

Mostly. If I had to do it again, I'm not sure I would recommend trying to graft chicks at 6 days old, I think I should have tried all of this as soon as I brought the new chicks home. The reason is that they tend to wander more for some reason (but that might have to do with the warmer weather so idk) which is why we have Nutmeg secured in a crate for now so her chicks can't run off. I think they'll all settle down alright though and get the hang of it, but I'm not sure the two mommies will be able to share space. Ash is very defensive, she attacks any hen who comes near. We'll see how things go. I'll update y'all again soon.