Maybe I'm not following things right, but instead of doing it this way, why not have the screen with email and password (and whatever else - forgot password, submit button, etc) - but have the screen do the check on the email - and if the flow is different, change the screen (remove fields, change labels, etc), or redirect to a new screen?

That way, those that use password managers could still continue so (as it would check and see that yes, password flow - or whatever), but for others, it would do something else.