Your thesis is guilty of an "either or-fallacy". You're concluding that either it's the same God, same laws OR it's different gods, different laws. But there's actually also a 3rd option, i.e., same God, different laws. The latter is the general Islamic position.. i.e., that different Messengers of the same God came with different laws suitable for their time/locale. That accounts for any differences in actions between any of the Messengers/Prophets. Btw, a lot of what you listed is also found in the Bible too including fighting, multiple wives, slavery, etc. It's not unique to just the Qur'an.

Before we can even address your question, you would first have to provide a source for what Jesus, may peace be upon him, said that is reliable and unaltered.

I would like to take a more conciliatory approach to answer this question by starting with some common grounds that Islam has with Christianity about Jesus:

1. That Jesus historically existed
2. That Jesus was a true prophet sent by God, the God of Abraham
3. That Jesus had the title "the anointed one" although understood differently in Islam as al-Masīḥ
4. That Jesus has the title the Word (Logos) although understood differently in Islam as kalimat Allāh
5. That Jesus was born without sin and remained without sin
6. That Jesus was born to Mary as a result of virginal conception
7. That Jesus performed miracles including raising people from the dead
8. That Jesus had foreknowledge of what was hidden to others
9. That Jesus is an important religious model, possessing the highest knowledge and intimacy with God
10. That Jesus was raised up to heaven (although this is not unanimous among Islam scholars)
11. That on the Day of Judgment (Yawm al-qiyāmah) Jesus will be witness against the wicked and destroy the anti-Christ (al-Masīḥ ad-Dajjāl)

But Islam denies the following Christian teachings about Jesus:

1. That the 4 canonical gospels faithfully recorded the teaching of Jesus and about Jesus. Instead, Muslim scholars consider the true gospel, Injīl, to be lost or hopelessly corrupted in the form of the NT gospels we have today, thus consider information about Jesus in the Quran as more authoritative.
2. That Jesus claimed to be the Son of God, with the full implications of what Jesus said to be understood in Christianity as,
   • being the second person of the Trinity and thus having pre-existence before conception
   • being fully divine yet fully human (i.e. Incarnation according to the Chalcedonian definition)
3. That Jesus was crucified until he was truly dead on the cross (see journal articles on medical evidence and a 2021 review of medical views). Instead, Muslim scholars's view is more similar to Gnosticism or Docetism (see the 2009 School of Oriental and African Studies journal article The Muslim Jesus: Dead or alive?).
4. That having truly died on the cross and buried in a cave tomb Jesus was raised from the dead on Resurrection Sunday. One interpretation of The Quran says that Jesus was not killed nor crucified but was instead raised to heaven alive. The Quran claims that people are only making assumptions about his crucifixion, and it was only made to appear so to them.
5. That the Counselor/Advocate whom Jesus sent in John 14 and John 16 is the Holy Spirit. Instead Muslim scholars understand Jesus to mean Muhammad (pbuh) (see here, refuted here).
6. That Jesus is present in Spirit in the world today (see What is the role of the Holy Spirit in our lives today?). Instead Muslim scholars understand Quran references to "Holy Spirit" (Rūḥ al-qudus) to refer to the angel Jibrīl (Gabriel) (pbuh). The Quraanic Exegesis article Who Is the Holy Spirit? concludes:

   So it is clear that Ruh al-Qudus here refers to Jibril… No one suggests that Ruh al-Qudus means the life of Allah ; nor is this indicated by the wording and this phrase is never used in that sense.” (Daqaiq al-Tafsir, part 2, p. 92)

Although Islamic prophet Muhammad (pbuh) spoke highly of Jesus as possibly greater than the OT prophets before him, and spoke highly of his mother Mary as well, all branches of Christianity cannot accept Muhammad (pbuh) on the same level as all canonized OT prophets and as the prophet Jesus himself because Muhammad (pbuh) denied that Jesus claimed to be the Son of God. Instead, Muhammad (pbuh) believed that Jesus, as a holy prophet sent by the true God, would never have "blasphemed" God by claiming to be God himself.

It's a pity that he probably got the wrong idea of the Trinity, thinking that Christians taught what we now call Tritheism (see Islamic view of the Trinity). Naturally, as Christians today ALSO denounce Tritheism as a denial of monotheism, this distorted view of the Trinity led him to exhort Christians to repent, such as in Quran Surah 5:116-118:

And [beware the Day] when Allah will say, "O Jesus, Son of Mary, did you say to the people, 'Take me and my mother as deities besides Allah ?'" He will say, "Exalted are You! It was not for me to say that to which I have no right. If I had said it, You would have known it. You know what is within myself, and I do not know what is within Yourself. Indeed, it is You who is Knower of the unseen. I said not to them except what You commanded me - to worship Allah, my Lord and your Lord. And I was a witness over them as long as I was among them; but when You took me up, You were the Observer over them, and You are, over all things, Witness. If You should punish them - indeed they are Your servants; but if You forgive them - indeed it is You who is the Exalted in Might, the Wise.

CONCLUSION: Since Jesus's being the Son of God whose true death on the cross and who is present in spirit in our lives today are both so central to salvation, and since true faith has to be based on agreeing with this, there is no way that any Christian can accept Muhammad (pbuh) as a true prophet despite many things he taught in common.

Christians trust that the 4 canonized gospels are the only authentic ones, that the other NT letters and books give us trustworthy accounts of what Jesus taught, trustworthy understanding of who Jesus is, and trustworthy interpretation of the OT. No true prophet would teach truths contrary to the truths presented in the Christian Bible.

Sources

1. University of Alberta Muslim Students' Association pamphlet Jesus: a Prophet of Islam
2. Vox 2019 article Muslims love Jesus, too: 6 things you didn't know about Jesus in Islam
3. U.S. Catholic magazine 2016 article What do Muslims think of Jesus?
4. Christianity Today 2002 article Is the God of Muhammad the Father of Jesus
5. Wikipedia article Jesus in Islam
6. Wikipedia article Names and titles of Jesus in the Quran
7. Wikipedia article Islamic views on Jesus' death
8. Wikipedia article Second Coming - Islam
9. Wikipedia article Messiah - Islam