Each line of the prayer is meant to assist us in opening our hearts, minds, and lives to the powerful presence of God who wills to work in and through each of us. So, if this is the case, and this Lord's Prayer is a model or paradigm of the very essence of prayer, the model or paradigm which represents "the mind of Christ" and the way we "put on the mind of Christ" then can we really argue there are "higher forms of prayer than petition"? To put it another way, isn't opening ourselves to another in love and trust the greatest praise one can offer another? And isn't petition, especially as Jesus articulates and orders these in any of the three or four versions we have, an invitation to genuine praise, namely, by putting God's needs first, and our needs/desires second? We are not, in other words, to being people who merely say, "Lord, Lord" (or "Praise God!"), but to BE (the) people who, petition by petition, give our whole selves over to God as the field from which God will bring forth the hidden treasure of God's Kingdom! In this way we are allowed to participate in God establishing God's very life on earth as it is in heaven. We are called, by every petition to open ourselves to the unremitting hallowing of God, to become, that is, living instances of Divine Praise!
One of the theologians who most influenced me when I was a young theologian myself was Gerhard Ebeling. Ebeling wrote a lot about theological linguistics and about human beings as Word Events. Each of us is called to become language events. An event differs from a mere occurrence in terms of meaning; an Event is something filled with meaning where a mere occurrence is relatively empty of significance. Like Jesus (though only in and through Jesus!!) we are to become incarnate Word of God --- meaningful Word Events created by and for God's Word, especially in the form of Proclamation. Most often I think of all of this in terms of becoming an articulate expression of the Gospel of God or becoming God's own prayer in our world. (Some theologians speak of Jesus as the Parable of God --- an identity that grounds and thus characterizes all he is and does, especially in preaching and teaching.) In light of what I have said about becoming a Word or Language Event, perhaps it would not be far off to suggest that we are to become articulate songs or hymns of Praise. As we pray the petitions of the Lord's Prayer, we open ourselves to the Presence, sovereignty, and will of God, don't we thus praise God in truth as well as in our words and become ourselves "Words of Divine Praise"? Could there possibly be a "higher" form of prayer?
I say this as a contemplative whose primary form of prayer is quiet prayer, but for whom other forms of prayer are meant to be equally contemplative, equally the work of the Spirit of Stillness or hesychasm. What I recognize is the dynamics of petitionary prayer and quiet prayer, for instance, are essentially the same: in each form of prayer we pose the question of (i.e., which is) our own incomplete lives and open ourselves to God's dynamic presence so that God might act within us, to touch, heal, strengthen, sanctify and complete us. Prayer is always God's own work in us. Isn't it time to let go of the notion of higher and lower forms of prayer?