I think the succession would pass to the most direct descendant of the last Tsar; therefore if Alexei and three others had died, the fourth, say, Marie would have been Head of House. That is why Anna Anderson was so controversial; if she had been proven to be Anastasia or one of the other Grand Duchesses, she would have been rightful head of House of Romanov, despite Pauline Laws. At the time, the only dynasts were the surviving Grand Dukes who were cousins.
So technically, a surviving daughter would be the rightful Head of House.
So technically, a surviving daughter would be the rightful Head of House.