What you sorte seems very reasonable.
The problem is you are not Atkins into account a few key data.
Having France build a new colonial empire ?
But the UK did not want this. It had fought and won the seven years war in order to destroy the previous french empire. This was not a cooperative world. It was, and this was especially true for the UK, a mercantilist world in which "I want all and the winner takes all."
The UK did not want France in India or North America. And it could and did stop them there. Stopping the French in north Africa is an entirely different ball game. For starters, the region is very close to France, and the ability of UK to intervene effectively there is much more limited. The real tragedy of the French is they never focussed on one region. They spread themselves all over the world and that was their major problem. While what you say may be true for the British, it is also true that Napoleon took too much from the continental countries. Without big continental allies, Britain would not be able to do a lot (other than naval attacks, but these were a double edged weapon). It was the fact that everyone else had signed a truce with Napoleon that persuaded the British to sign the peace of Amiens.
Having France be satisfied with its Rhine frontier ?
You are right. It should have. But the UK would not have. France holding Belgium and Antwerp was a casus belli for the UK.
In the treaty of Amiens of 1802, the brits only "tried" the peace solution because it was on the edge of a popular revolt against its oligarchy and needed time to rest and rebuild its forces.
No - but he had always had grand pretensions. He crowned himself with the Iron Crown of Lombardy in Milan, frightening Austria about the meaning of the act. Then, there was the murder of the Duc d'Enghien (c'est pire qu'un crime, c'est une faute!). But the real reason was that Napoleon had taken too much from Austria in the previous wars (what was the point of taking Dalmatia or Ionian islands, or even Tuscany, in the treaty of Luneville?), and the Revolution and its acts had terrified everyone. Napoleon, more than anyone else, had to be more careful than the other aristocrats - they did not intend to change the format of rule. The revolution did. Napoleon could and should have pacified Austria, at least. And without Austria, Russia would not have entered the Third Coalition. Operating against France from Russia is a tad hard ....
Before its invasion of Spain in 1808, Napoleon never triggered hostilities. The UK forced war on France and Napoleon. And since every previous peace treaty appeared to be a joke, Napoleon felt its only solution was to take more territorial guarantees. In some way, as you noticed, this was a dead end. But this apparent dead end would have in fact worked if Napoleon had not messed everything up with his disastrous russian campaign (I don't mean disastrous war since war with Russia was unavoidable in 1812 but I mean the disastrous way Napoleon led his campaign, abandoning the sound strategy he had initially conceived and losing his army in the russian gigantic territory.)
I am not sure it would have worked. The German situation was going into a tizzy, and Austria re-entered the war in 1809, although they were badly bruised in 1805. The situation Napoleon had was anything but stable. He had had a chance at stability in 1802. He should not have lost it. Even a war with Britain should not have brought the others into a Coalition against France.
The league of neutrals ? It was useless against the UK. The UK of the early 19th century was all but a democracy. It did not care about public opinion. Especially not foreign public opinion.
A coalition is always weaker than a single great power, on sea as well as on land. The british on sea used the watchword "divide and crush". They crushed Denmark when they felt they needed to. And the message sent was very efficient with other neutrals.
Not quite. If Napoleon had played his cards correctly, it would be the British who would be forced into more suicidal acts like the attack on the Danes. Russia and Denmark had been considering a Baltic naval alliance, to stop British attacks on their fleet. For Britain, blockades were always extremely expensive affairs, diplomatically. Seizing Austrian, Prussian or Russian ships sailing to France would damage them far more diplomatically than anything France could do. And while Britain might not care very much what they others thought, she was always anxious never to be left without any allies on the continent. As the British kept launching their attacks on the neutrals, more and more would be implementing their own version of the Continental policy, without any prodding from France.