Our Father/Mother in heaven
Oh my goodness, I can't even...
While this is probably inappropriate for the Lord's Prayer, there's an extensive tradition in medieval theology and mysticism of using feminine as well as masculine terms and imagery for God. I think it's Margery Kempe who talks at one point about nursing at Jesus' breast. Gregory of Nazianzus specifically mocks the idea that the Father's fatherhood implies the same things about gender as human fatherhood (the Son's sonhood has generally of course been seen as much more gendered in human terms, on account of the Incarnation).
Yeah, I mean I don't want to say that God is definitely a man and doesn't have feminine qualities, or certainly that men are closer to God than women are. But cmon, just use the language our Lord gave us. Use the imagery he gave us. Don't try to achieve some unnecessary ultra-feminist goal at the expense of understanding what the Lord has given us. God is the Father. Jesus is the Son. Mary is the Mother of Christ. Jesus is the bridegroom, and we, the body of believers, are the bride. Women shouldn't feel any less close to God because of the language, but there is a reason that language was used.