Mommy! and granny! really wonder if grandma suspect he's the same person from the past, because she has been more open to it than the mom and in both cases is "taboo", I mean... she was already more open to sex when she was young, but I remember that in the Artifact the grandma was the one who knew he went to the past, maybe it's the same here.
It's clear the story with mom will not advance too much in the present, they will do the whole TimeStamp thing and she will fall in love with him in the past, making things easier for him in the present.