I'm not a Calvinist but I do not see any contradiction here. According to what I understand, Calvin says we are all sinners, which we are. Of course we believe first, and we obey, hence do our best not to sin but we fail again and again, even if only invisibly, in our minds and in our hearts (judgement, resentment, lack of compassion...). It is hence clear that we believe but we are not established in our faith since our actions, words and thoughts are not in tune with our beliefs. If we try hard enough and if our actions, words and thoughts become closely tuned with our beliefs, then we will have real faith, we will walk our talk, and God will save us. This is how I understand the little bit of Calvin's teachings you quoted. Being baptized is not enough, believing is not enough, we must work hard to be saved.
This point of view is sustained by James 2:14-24 which is very clear about the importance of good deeds. It ends with: "You see that a person is considered righteous by what they do and not by faith alone".
Of course, you could find verses from Paul saying the opposite but Paul and James are in blatant contradiction on the subject of salvation. One could argue Paul doesn't oppose James on the subject of salvation because Paul assumes our actions will always be good if we have faith but this is wrong. Who among us can say they never sinned from the moment they converted?
When it comes to salvation, Christians therefore clearly have to choose between Paul and James. I have no idea why anyone reading Paul carefully and with an open mind -- e.g. setting aside the preconception that everything Paul wrote is the truth -- would believe Paul: James was chosen by Jesus, Paul wasn't. James spent lots of time with Jesus, Paul never met Jesus. I have never read James contradicting himself and I have exposed, in recent posts in another thread, some of Paul's contradictions and inconsistencies. I have also pointed out that Paul's spiritual understanding can be shallow at times.
Now, James is not the only one proving Paul wrong on the topic of salvation. Even John the Baptist refused baptizing Pharisees and Sadducees unless they would produce fruits worthy of repentance (Matthew 3:7-9; Luke 3:7-8) which clearly means that believing and repenting is not enough.
This is an interesting proposition you make.
I would make a simple point. I often say a sentence, which is one context means one thing and in another something else. Words, grammar, order, hierarchy change meanings, and when you layer everything together, you may find James, John, Paul, Jesus are all saying the same thing.
As a believer I have gone through many different emphasises and found while I discover one, it appears to explain everything, but when it falls into context, it becomes part of a whole. Paul said something strange. I can eat food sacrificed to idols, because idols are just stone, and it means nothing to me. The apostles though wanted gentiles to not do this in their encouragement to them in Acts when they accepted a believer could be a gentile and not also a jew.
I have had many conversations with ex-legalists who are hyper sensitive to any rules which might condemn them. Often they are nice folk with much love for those they meet, yet for them they were wounded by self righteousness and self justification which they followed for many years. In a discussion they would not murder someone, and expect forgiveness, but they do not want to condemn themselves for speeding. For them building a christian culture is wrong, they are saved sinners because of Jesus. What they often miss is sinners who really live without rules are lost, and know nothing of love and care, which in words is the world they are claiming Jesus accepts.
These different emotional reactions to ideas, mean a short interaction on the internet will not change people or their positions, but can open the door to meaningful dialogue, and the assertion that praises Jesus.
Paul believed in showing repentance in a believers life to demonstrate the real reality of the Holy Spirit.
"I preached that they should repent and turn to God and prove their repentance by their deeds"
Acts 26:20
Paul believes the structure of being a pharisee does not justify a believer, but he upholds the law through living by love. It is possible to take some of Pauls words and make it sound like he is against morality, and faith in Jesus saves us. The classic problem is "faith in Jesus" does save us, but this faith shows itself in a changed life following Jesus and His words. Some followers I have met have a single sheet of A4 paper as their gospel. This is a faith of summary and simplification because anything more for them is too much and they cannot cope.
Faith is often about coping strategies, rather than finding the truth, or balance or changing ones heart from the inside out. Some called me evil, a marxist for suggesting you need to love from the heart, except that is Jesus's words.
I have concluded that emotionally we make a world in our heads we can cope with, even though the logic is wrong, it is who we are, and we will defend it come what may. One believer who had suffered from depression etc. found his faith gave him hope, so what he saw as a challenge was painful to him. Sadly I was just repeating Jesus's words, so whatever he had made Jesus into, it was not Jesus of scripture.
God bless you