Could you give your opinion on where I went wrong and he understood it correctly, or vice versa?

I’m not familiar with his argument, so I can’t give an opinion.

1. There is a general position that attributes history to the governance of the Holy One, blessed be He (success is a sign of divine choice, and vice versa). Therefore, from the fact that Israel conquered the land, it follows that the Master of the whole world decided that this is what He wanted, and therefore the land belongs to Israel. That position is refuted by the fact that in exactly the same way, the Holy One, blessed be He, also decided that the land would be in the hands of the Assyrians, Babylonians, Persians, Romans, etc. (so that position was irrelevant in ’48). And furthermore, such a position has no power to prevent an aggressive invader (who accepts the position!) from invading and attacking, because if he succeeds, that will prove that this is the will of the Holy One, blessed be He (so the position is irrelevant in 2021 as well). That is probably what Leibowitz argued. I haven’t seen the film, but I vaguely remember reading an argument like that in one of his books.

2. But of course this has nothing to do with Rashi on Genesis. The Torah simply says that the Holy One, blessed be He, promises the land to the descendants of Abraham, and it also describes that even after He exiles them, He will return them. So the conquest of the seven nations is by the direct will of the Holy One, blessed be He, and the return from the exiles is by implied will. In other words, “the land is ours” not because it is proven from the fact that the Holy One, blessed be He, enabled us to conquer the seven nations, but because it is written in the true Torah that the Holy One, blessed be He, grants us the land.

3. Rashi says: “By His will He took it from them and gave it to us.” If the taking and the giving are the proofs of His will, then that is the first position, and it doesn’t hold water. But if His will is known from the Torah even without the taking and the giving, then that is the second position, and that is of course what is written in Rashi (because if the proof comes from the giving, then you don’t need the Torah starting from Genesis — and the whole point Rashi is making there is to explain why the Torah is needed).

4. From religious faith it indeed follows that the Holy One, blessed be He, gave the land to the Jewish people (just as He gave me the cup sitting on my table right now with a little puddle of tea at the bottom). Is the claim that the land “belongs” to the Jewish people relevant, interesting, and consequential? In my opinion, no — but that’s already a different discussion.

By His will He gave, and by His will He took.

As long as the first commandment, “This month shall be for you,” is not being fulfilled and the first of the months is the month of Tishrei, you have no claim at all.
God gave the Land of Israel to whoever fulfills “This month shall be for you,” and not to a bunch of riffraff who do whatever they feel like.

He meant that a people has no natural right to a land. Does a plot of forest belong to the first tiger that got there?

If the Holy One, blessed be He, granted that plot to that tiger, then yes.

Indeed — but not by natural right.

And because Rashi’s first comment on the Torah is not talking about a natural right (that is, a right by virtue of the takeover itself — and he also does not say that the takeover is a sign of divine approval), but rather about a right given directly by God, starting from the Covenant Between the Parts to the descendants of Abraham and onward, then from the traditional Jewish position it indeed follows that the land belongs to the Jewish people.
The Last Decisor argued that even according to the religious position, the land belongs only to members of the Jewish religion and not to members of the Jewish nation. You can base that on the fact that the Torah and the Prophets repeatedly warn that the land will vomit out sinners. But it is certainly possible that in terms of ownership the land remains Jewish property (even if they sinned), while the Holy One, blessed be He, brings about their expulsion from it, which is like an external limitation and not confiscation of ownership.

There is certainly a lot of room for the position that a plot of forest belongs to the first person who decided to be its owner. Of course, the boundaries have to be discussed, and a person cannot declare the entire unclaimed world as his plot. But Israel, after the forty years in the wilderness, were not “a people without a land coming to a land without a people,” the first to arrive at some forest plot; they conquered it through blood and fire. So there is no claim based on being first, and no claim based on conquest itself, but rather a claim by virtue of divine right.
Why does the land belong to God, and why does He have the authority to distribute it? Because He created it. Of course, that too can be challenged.

A plot of forest belongs to whoever wants it to belong to him and is more violent and stronger than the other guy who also wants it to belong to him.

Natural right = might makes right.

Declaring ownerless land to be “mine” is irrelevant in terms of property law. What matters is performing homesteading. The Creator of the world is the homesteader of the universe par excellence, and therefore the legal owner of the territory of Israel and can decide to whom to hand it over.

Even without that, the Jewish people performed homesteading thousands of years before the Roman conquest, and therefore are the legal owners of their land, and ever since then have always claimed ownership over it.

The Last Decisor,
In the Torah, the beginning of the months is not the same thing as the beginning of the years, and Nisan is indeed the first of the months for us.

In reality, there is territory.
You can define ownerless land as land where no one will attack you if you settle there.
God doesn’t dance to the tune you play unless He came to you looking for work and you hired Him as a homesteader, and if so then you’re obligated to report it to the tax authorities.

In the Torah there is no month called Nisan; there is a first month. It is first of the months of the year, meaning it is the New Year.
Your evasions are not serious at all.

From God’s nature derive the definitions of good and evil (including what is a good deed and what is an evil deed), just as all necessary abstract “entities” derive from it (propositions, the laws of mathematics, logic, possible worlds).

You’re making a logical leap here. See Leviticus 25 regarding Sabbatical years. The counting of years certainly begins in the autumn. Show me one place in the Torah or in the Hebrew Bible at all where it says that Nisan is the New Year.