That sounds like a serviceable way to get a US government overly cocky about its ability to throw its weight around and intimidate others. Trying to power play or truly take risks for Pernambuco still seems a stretch, as does doing it successfully, but this seems a fairly decent set-up for it.
I would wonder if the kind of set-up you suggest and provide here, of a blustery USA getting the British to back down on the Orders-in-Council issue and preventing the War of 1812, does not leave idle American hands free to make mischief, and minds at ease to grow ambition, to solve the "Florida problem" in much more of a hurry, and perhaps greedily attempt to leverage Spain's troubles to possibly reopen and solve a Texas problem, Alta California "problem", or Cuba "problem" with a Spanish-American war at some point between 1813 and 1818?
As I was suggesting, in this case, the US would simply give in to temptation to resolve the Florida problem by declaring war on Spain, invading Florida, and annexing it, instead of negotiating the transcontinental treaty. So it forces minimum concession from Spain in that war of Florida/Florida(s), and probably Spain's claim to Oregon Country as well, while not making any concessions to Spanish New Spain for the western "step boundary" adjustment to the Louisiana Purchase/Unorganized Territory. However, depending on ambition, luck, and intrigue with Mexican and Spanish-American independentist forces, the US may succeed in further territorial expansion in an anti Spanish war. Gaining Texas- perhaps its eastern part up to the Colorado, or a boundary all the way to the Rio Grande. Or have further remarkable success and claim all Nuevo Mexico and Alta California, possibly while supporting Mexican rebels to the south. Or gaining cession of Cuba....but here I have no idea of the US-Spanish naval balance or imbalance at the time. Cuba could easily be an operation eminently sinkable by Spanish squadrons, depending on the timing.
