I think I’ve figured out a way for the US to win the war without ASB action after the British declare war on the US over the Trent Affair:
There were only about 20,000 British regulars in Canada in December 1861 and the British generally agreed they wouldn’t be able to make any move against the US until spring 1862. This provides the US with a 3 to 6 month window in which it can act without British intervention.
No, there are about 5,000 regulars in the Province of Canada, they were reinforced to ca. 20,000 during the 3 weeks the British were actually preparing for war. By no means had the reinforcements stopped flowing. 75,000 regulars were set in motion on 7th December 1861. The frozen St Lawrence River meant that the speed they could reach PC was limited, but nothing could stop this force reaching Halifax or Bermuda as a staging ground.
Attacking Canada in January is a bit like attacking Russia in the depth of winter. The country will eat armies.
So, knowing this, and realizing the British must be defeated before they can make their weight felt, Lincoln and the Union generals decide on a Washington-esque plan. 40,000 Union soldiers are gathered, either spit off from the Army of the Potomac or grabbed in penny packets from wherever they can be found, and formed into the Army of the St. Lawrence under the command of some skilled general like Reynolds or Grant (probably neither of these two but someone of their caliber).
Banks and Burnside have the seniority and are commanding the departments facing Canada. They will command any invasion force down the Hudson Valley route.
40,000 Federal soldiers is a lot for January 1861. It's more than half the Army of the Potomac's disposable force (152,000 present, 32,000 sick, 50,000 required for the defence of Washington = 70,000), and larger than any other Army fielded by the Union (few of which top 20,000).
After a daring winter march, inspired by the Battle of Trenton, the Army of the St. Lawrence attacks the British army in Canada with a 2:1 advantage in regulars.
Regulars? How is a civilian volunteer with a few months in service and very little actual training, which is entirely confined to pseudo-Prussian drill, and an old smoothbore (possibly still a flintlock at this stage) constitute a regular?
In fact the Federal Army is essentially a mobilised militia, with all the problems entailed. They're not likely to perform better than the Canadian militia (who have rifle-muskets and British instructors on how to use them properly). Throwing 40,000 Federal volunteers against 20,000 British regulars and 100,000 Canadian volunteers doesn't sound like a good idea. Especially in mid-winter, when the troops will freeze and you have no supply lines.
The mass of Canadian militiamen only serves to disorganize the British/Canadian army
The Canadian volunteers were trained much harder than the pre-war US volunteer militia, with modern weapons. Clumsy as they're likely to be, they certainly no worse than the Federals.
Simultaneously every American naval and merchant ship with a pop-gun hits every British merchantman it can find, with a possible shelling of the British Isles just for the psychological effect.
You do know most British Atlantic steamers were "fitted for but not with" some quite heavy guns. Sure, but a couple of 12 pdrs on a schooner, but see how well they'll fare against a mail packet with 6x 68 pdrs.
I would like to point out, because someone is going to criticize this, especially the Army of the St. Lawrence’s march part, that it is actually fairly logical and justified by a bona fide American legend: Washington Crossing the Delaware. The campaign’s logic is also fairly similar to the German’s in 1918. The British, no offense to them, did not have the best generalship so being beaten while outnumbered 2:1 against a fairly well-trained army is also not that unlikely.
You do know the British actually won the Kaiserschlatt?
The majority of the Canadian militiamen were badly trained and would probably disrupt the British army and add to the casualty count.
but better trained, armed, equipped and led than the Federal army.
The British Navy would also be unable to win a decisive victory over the US Navy since the USN would operate completely un-concentrated like it did in 1812.
You do know the US ships in this period are much, much weaker than their RN equivalents? The US just doesn't have the heavy engineering expertise of the UK.
Faced with, as I said, an unpopular losing war with nothing to gain, the British probably would bail out if the US offered a white peace, scapegoat some minor generals and on the whole pass it off as a minor colonial disaster like the later Battle of Isandlwana.
That was a minor engagement (essentially a single battalion), and Britain's vengeance was the destruction of a nation.