Astrid knows it's not looking the best, but due to her pride, she's still going though with her plan. She figured it was now or never, and as a "chosen ruler" the gods would be on her side.
Tyris-She first asks Tyris. Tyris thinks for a moment before agreeing rather assuredly. "You know, I've been living on borrowed time for a while anyway. If I die, maybe I can die finally trying to do something for the right reasons," she says.
Mireilla and Arastine-Her next prospect is Mireille, where she says "Listen, there's no way I can free the slaves since Toxin would still be the big boss, but I can surely make things a hell of a lot better for them around here," along with assuring Augusts methods would no longer be allowed, and urging that she try to convince Arastine immediately after to join the mutiny as well, despite finding it unwise to ask it herself. The two were often at each others side though so she had prepared to ask both nonetheless in case it was needed. She'd let Tyris try to convince Arastine as well, with her talk about how Marla is doing almost the opposite of keeping her people safe.
Millie-After that was Millie, who was afraid and didn't want to be there. Astrid planned to assure her that the only way to be safe is to help her kill Marla so Astrid could keep her out of the front lines.
Hathus-Then Hathus, who was heroic, and seemed to have a slight distaste for what he was doing. Again, she planned to assure this would change a bit with Marla out of the picture.
Mckayla-Finally McKayla, who Astrid had a slight lie prepared for. "You know how Aura isn't acting like herself? I overheard Marla say that she's going to put you in a trance like that next!"
Astrid's list of candidates were in order from the ones she considered the safest to ask, to the least safe. When someone might except, she essentially add them to her party, and take them all along to the the next candidate, adding a bit of a peer pressure element to it. If anyone threatened to tell Marla, they would simply hurry up the process and enact the planned assassination as soon as possible.