But nowhere in the Gospels does Jesus ever suggest redemption through faith. Everything Jesus says is entirely consistent with the Old Testament. The idea of God's forgiveness by sincere repentance comes right from the Old Testament. On the other hand, I hate Paul. What he says seems contrary to both the Old Testament and the teachings of Jesus. Paul brought up the idea of redemption through faith. And then Martin Luther threw out all that was good about Christianity with his sola fide idea. Anyway, that's my understanding.
I think you're doing Paul an injustice. Romans is focused on a specific problem: claims that in order to become a Christian, people have to accept the Jewish law. He is not concerned with people claiming that you can be a Christian without doing anything about it. This leads to a one-sided focus. But in other letters he is just as insistent as Jesus that Christians have to show their faith in action.
Jesus doesn't use any term like justification by faith, nor does faith play the same central role for him that it does for Paul. But he has an equivalent concept. I believe if you read through all of Romans, and not just the proof texts, you'll find that Paul thinks there is a fundamental orientation to our lives, which he calls faith, but also other things. Jesus says this too. He's inclined to speak of people being his followers, servants, or of being members of the kingdom. Remember all those parables where people are told to sell all they have to get the pearl of great price, which is membership in the kingdom. He also uses the family terminology, with God as our father.
Jesus is also very concerned about motivation. While he speaks of obedience, when it comes down to looking at specific ethics, he tends to interpret the Law very freely, looking at intent. And he sees the Law summarized in loving God and neighbor. So although Jesus is very focused on action, he is also focused on where action comes from.
I think you can unify Paul and Jesus, with some difficulty I admit. Both see actions as important. To see that in Paul you need to look at something other the Romans proof texts, but it's there. But both see actions as coming out of a fundamental orientation, which is justification / faith for Paul and being followers / members of the Kingdom, having God as our Father for Jesus.
Why does it matter that action comes out of a fundamental relationship or status? Because if actions don't follow from some consistent approach of loving our neighbor and following God, they're too likely to become legalistic. But more important, if there's no continuing status, there's no way to deal with failure. Jesus focuses on two things: the need for obedience, but also the love of the father for his people, which lets us deal with our failures. Without the continuing status of being one of his people, there's no basis for God to continue dealing with us even when we fail. You can't take Jesus' emphasis on obedience and separate it from his emphasis on the Father's love for his people and his desire to forgive.
The prophets have the same thing, although much of it is implicit in the context in which they operate. The prophets do more than demand right behavior and threaten national punishment. They also speak of God as a crazy lover who keeps loving his people despite being jilted. The implicit (and sometimes explicit) context is that they are speaking to the covenant people, who have a permanent status as God's people. It's that status of being one of God's people, in a Christian context where God's people are no longer a specific nation, that Paul means by justification and Jesus means by being his followers.
Paul's specific task was making the transition from God's people as one nation to God's people as all of those who have faith in Christ. As N T Wright says, for Paul faith has the same status as the badge of membership that birth within the covenant people (or circumcision) has in the OT. During his life, Jesus preached primarily to Jews, so he didn't as explicitly face this problem. He did define the Kingdom as all of his followers. So he certainly did nothing to suggest a continuing use of the old national covenant. But he didn't explicitly talk about changing the primary marker of covenant membership from the circumcision to faith in Christ. If you prefer, read following Christ rather than faith in Christ. That aligns it more with Jesus' terminology, but it's the same thing.
If your concern is that Paul isn't closely enough aligned with the OT, I suggest looking at the most recent generation of Pauline scholarship. The most visible representative of this is N T Wright. He understands Paul's justification and righteousness in OT covenantal terms. While I think he's a bit one-sided, there's a lot to be said for his understanding of justification.