Wheat versus rice is precisely a matter of "faith and submission". Unleavened wheat bread was what God commanded for the Passover. Jesus, in obedience to his own commandment, used wheat. Therefore we use wheat.
As you correctly said, "faith" and "submission".
Your response makes my point.
We use wheat because it's doctrine that we use wheat. There's nothing wrong with that, and even some very good things about it. But remember also that the Jewish dietary laws don't apply to us. More importantly, the flour with which the host is made is not a matter upon which eternal life depends. It's our faith that matters. The sort of faith God is looking for does not depend on the use of wheat flour: he's more interested in how we approach the altar.
What we have then, is a rule that by which some choose to define "valid" and "invalid" Communion, as if God really cares about what kind of flour we use. Jesus said of such people:
They tie up heavy burdens, hard to bear, and lay them on people's shoulders, but they themselves are not willing to move them with their finger. (Matt. 23:4)
Taking it further, suppose wheat wasn't an option for some reason. Is Communion therefore impossible? Highly doubtful. Jesus told the following story:
And he said to them, "Have you never read what David did, when he was in need and was hungry, he and those who were with him: how he entered the house of God, in the time of Abiathar the high priest, and ate the bread of the Presence, which it is not lawful for any but the priests to eat, and also gave it to those who were with him?" And he said to them, "The Sabbath was made for man, not man for the Sabbath. (Mark 2:25-27)
Jesus' point is that rules and doctrine are not ends in themselves; rather, they're supposed to help people toward a relationship with God. Doctrine should never be used to block our path -- but that's very often what "doctrinal fights" end up doing.