Allow me to re-align the question a little bit before answering. None of the religions is really an "update" as such. There is nothing lacking or imperfect in either Judaism or Christianity, or the message or scripture or Law of any of the Prophets (upon them all be peace and blessings). The only reason they are different is because

1. They are meant for different groups of people at different times. Judaism was meant specifically for the Children of Israel between Moses (peace be upon him) and Jesus (peace be upon him). They had a different law for the time of Abraham (peace be upon him) and Jacob (peace be upon him). Christianity was also meant for the Children of Israel, between Jesus (peace be upon him) and Muhammad (peace be upon him). Islam as brought by the Prophet Muhammad (peace be upon him) is unique in that it is the final revelation, for all of mankind until the end of time. There were other Laws brought by different Prophets (Noah (peace be upon him) for example, and others too), that were meant for a specific nation at a specific time.
2. Both Judaism and Christianity were corrupted by man. We believe Judaism was corrupted by the rabbis of the Children of Israel to suit their whims and desires. The Qur'an accuses them of literally changing the Word of God. The Christians, similarly, strayed from pure monotheism and instead made their prophet divine, in the process attributing a son to God (far above is He from such things).

The reason for any similarity (less or more) between Judaism and Christianity and Islam is because they are all from the same source. Theology-wise, they were revealed identically. There is no difference between (pure) Islam, (pure) Christianity, and (pure) Judaism when it comes to theology. The Law is slightly different from one to another, and we don't know fully why that is. We do know for example that the progressive harshness of Judaic law was because of the transgressions of the Children of Israel. There may be other reasons as well.

As for why modern Christianity looks so different from modern Islam and Judaism, it may be more instructive to look at a different question: how different is modern Christianity from Jesus-era Christianity? We don't believe that the trinity was originally part of Christianity, and we don't believe that the entirety of ceremonial law was abrogated with the coming of Jesus (peace be upon him). So we believe (and this is borne historically) that modern Christianity is very very different from early Christianity. Judaism also underwent changes, and Islam even less so. Islamic theology is preserved in the texts word for word.

With that background, to answer your final question - 1) there is no question of intermediate steps and 2) Islam does not retreat from the differences between modern Christianity and Judaism - the following may sound pretentious, but it's not me, it's God saying so - rather, Islam corrects them.

And Allah knows better.

Allow me to re-align the question a little bit before answering. None of the religions is really an "update" as such. There is nothing lacking or imperfect in either Judaism or Christianity, or the message or scripture or Law of any of the Prophets (upon them all be peace and blessings). The only reason they are different is because

1. They were meant for different groups of people at different times. Judaism was meant specifically for the Children of Israel between Moses (peace be upon him) and Jesus (peace be upon him). They had a different law for the time of Abraham (peace be upon him) and Jacob (peace be upon him). Christianity was also meant for the Children of Israel, between Jesus (peace be upon him) and Muhammad (peace be upon him). We know this because the preaching of all the Prophets and Messengers from the nation of the Children of Israel was directed at themselves - they were never directed to preach to other nations, even neighboring ones. Islam as brought by the Prophet Muhammad (peace be upon him) is unique in that it is the final revelation, for all of mankind until the end of time. There were other Laws brought by different Prophets (Noah (peace be upon him) for example, and others too), that were meant for a specific nation at a specific time.
2. Both Judaism and Christianity were corrupted by man. We believe Judaism was corrupted by the rabbis of the Children of Israel to suit their whims and desires. The Qur'an accuses them of literally changing the Word of God. The Christians, similarly, strayed from pure monotheism and instead made their prophet divine, in the process attributing a son to God (far above is He from such things).

The reason for any similarity (less or more) between Judaism and Christianity and Islam is because they are all from the same source. Theology-wise, they were revealed identically. There is no difference between (pure) Islam, (pure) Christianity, and (pure) Judaism when it comes to theology. The Law is slightly different from one to another, and we don't know fully why that is. We do know for example that the progressive harshness of Judaic law was because of the transgressions of the Children of Israel. There may be other reasons as well.

As for why modern Christianity looks so different from modern Islam and Judaism, it may be more instructive to look at a different question: how different is modern Christianity from Jesus-era Christianity? We don't believe that the trinity was originally part of Christianity, and we don't believe that the entirety of ceremonial law was abrogated with the coming of Jesus (peace be upon him). So we believe (and this is borne historically) that modern Christianity is very very different from early Christianity. Judaism also underwent changes, and Islam even less so. Islamic theology is preserved in the texts word for word.

With that background, to answer your final question - 1) there is no question of intermediate steps and 2) Islam does not retreat from the differences between modern Christianity and Judaism - the following may sound pretentious, but it's not me, it's God saying so - rather, Islam corrects them.

And Allah knows better.