Yeah, Early Bird is probably better. I just added Tangled Feet as an option if someone wants to use Thrash. I'll edit the set.
As for the other egg moves, I agree that Haze and Brave Bird are the only mandatory ones. But I honestly don't think that Natural Gift, Flail, or Mirror Move are more useful than Feint Attack and Assurance (I think they're all equal in their uselessness). But since these are just filler moves anyway, I'm okay with picking the 2 most wanted by the group. I'll wait for others to respond.