Speaking with an auto mechanic friend of mine, he expressed frustration. He said that he knew exactly what the car was doing wrong, but had no idea why it was doing it, and thus no idea how to fix it. He described to me the two or three usual methods of performing this repair job, and none of them had been successful (it was a very odd situation). I believe that he eventually figured it out, but until he knew exactly what was happening, he did not know how to do the repair. Car repair is not the only time that this kind of problem arises in our lives; we always need to know what is wrong before we can know how to fix it.
As we seek to examine that first detail of "how" to move forward towards a godly "new normal", we have to acknowledge that God's word comes first, and our own ideas can never be allowed to do so. In other words, in many of life's challenges, our Lord has already laid out a plan for how to deal with things, but we frequently ignore it and choose to follow our own (human) wisdom instead of God's (divine) wisdom. Step one in learning how to be faithful is admitting that God knows more than we do and then doing our best to act accordingly.
Therefore, if we are asking the question as to "how" we accomplish a new normal that accords with the Kingdom of Christ, we must first see the way that His Kingdom actually grows. Many times in Scripture we are told that the Kingdom of Christ is (at least for now) a spiritual Kingdom (predominantly). This means that the Kingdom of Christ does touch on the physical realm; it is just as much a law of Christ that we do not commit adultery as that we be reverent when in the presence of the Eucharist. The primary means, however, for the growth of the Kingdom of Christ in this world is spiritual.
The Kingdom grows through changing men's hearts first, and then afterwards it changes society's laws, for only when hearts have changed can societal norms and laws be fully effective. Therefore, we need to be very cautious when we are seeking to make "physical" changes to our surroundings, so that we ensure that we are not making those changes our first aim (not that we should not make those changes, but that they need to be kept in their proper place). To be specific: influencing the political realm is important, but it is not our first and most important work. If your membership in a political party is more important to you than your Church membership, then something is seriously wrong with your faith.
In fact, this necessary balance is so crucial to the work of the Kingdom of God, that we could say that the local society will develop rightly if the Kingdom of God is already growing. This is so because the Kingdom always impacts the institutions around it. Even societies that are heavily influenced by wickedness can be changed by just a few faithful within that society (think of God's willingness to spare Sodom and Gomorrah if there were "at least 10 faithful people in the city"). It might take some time, but the Kingdom of Christ always wins in the end.
As the world systems develop and change over time, the Church should be the primary influence on those systems. This is, obviously, not always the case, but it is the ideal that we are supposed to aim for. When the opposite happens, we are in trouble. Today, we find that many in the Catholic Church (both laity and clergy) are listening to the world and worldly wisdom (sometimes equated with "science") more than to the Word of God. Whenever this happens we will see people within the Church trying to abandon the past and change Church teaching (e.g. much of what is coming out of the German Bishops these days).
Politics and political theory should not be excluded from this. It is not a neutral practice that is allowed to go any direction the people desire. The Church has spoken about political theory in various places, and although she does not advocate one political system over others, there are a few practices that she has directly stated are evil (such as socialism!). Therefore, politicians and those involved in civil leadership should be looking to the Church and asking what is the right way to do their job, but that is not what is happening. The fault is not entirely with the politicians; it can also be found in the fact that many (even Catholics) are treating the political sphere as though it were the ultimate authority in society. NO; as in "N", "O". Not true; never was, never will be.
Once we begin to see clearly in our heart, soul, and mind, how God wants us to move toward holiness (in the spiritual realm first, and the physical realm as a direct consequence) then we will be able to move forward. As with my mechanic friend, if he used the wrong method to repair the car, he would not have gotten far. The Catholic Church as a whole is currently not doing well at growing in holiness, which implies we are not using the right methods. Do not ignore the physical realm, but also do not allow it to become the primary means of spreading the Kingdom of God.