Like I said, we lost the war. We also lost in Vietnam. And Bill Clinton got impeached. Reagan Won the Cold War. Thus endeth the class in America History 565, What the History Textbooks Don't Like to Talk About.
Incidentally, America LOST the War of 1812. Had England opted to go for it, they could have reclaimed her former colonies, but they were rather more worried about that Bonaparte chap.
While many of your claims regarding objectives are true, I challenge strongly the assertion that England could have reclaimed the "colonies" if she had a mind. The victory in New Orleans, had it occurred before the treaty, would have certainly led to more favorable peace terms.
As it was, the fight was more or less a draw. While it is true we did not defeat the English Navy on the high seas in ernest, several victories (Constitution, UNited States, and Hornet) were important. Even more so, the defeat of Barclay on Lake Erie by Perry was significant and a shock to the British (Perry's quote will ring through history, "We have me the enemy and they are ours"), and the defeat of the British fleet on Lake Chaplain by Macdonough at Plattsburg Bay stopped the invasion of the U.S. in progress by Provost (which was essentially a repeat of the Revoultionary War effort to split the nation which also failed). All in all we did enough damage and made enough of a name for ourselves from a naval perspective to have the English want to put an end to it through negotiation, particularly given their other involvement and despite the success of their blockade.
They did invade and burn Washington, but they were rejected and ultimately defeated on the ground, near Moraviantown in Canada when Harrison beat the indian conferdration and the English General Proctor, by Scott at Chippewa and by Jackson at New Orleans.
So, though many of the strategic issues you speak of are true, I believe I would not count the War of 1812 as a victory for the British. Once engaged they intended to invade and defeat us and they tried to do just that. But they were defeated on the ground and suffered on the sea, particularly inland. And I believe had New Orleans occurred before the treaty, that the terms would have been more heavily weighted to the U.S as opposed to the "draw" it essentially turned out to be.
So, while I believe many of your points are accurate and correct in terms of the strategic situation, I still take issue with the notion that the English could have even come close to "reclaiming" he foremer colonies in the least. That was the essential point of my post.