Let's see...
All the ships in the British squadron off Norfolk were already in the Americas as of the Trent affair, with the exception of those which OTL were sent as reinforcements. They're all in the NA&WI Squadron, so don't need to cross the Atlantic; their times of arrival at Bermuda are as OTL; thus, they could turn up off Norfolk at the time I have them doing it.
War warning as per plans, 8 Jan, Bermuda. Milne orders concentration.
9 Jan, War declared.
20 Jan, war confirmation arrives at Bermuda.
21 Jan, US gets confirmation that war is declared.
25 Jan, Milne sets sail from Bermuda.
Hero, Donegal, Agamemnon, Aboukir, Immortalite, Melopmene, Liffey, Spiteful, Rinaldo, Medea, Cygnet and
Racer were all NA&WI squadron - it's only a matter of getting the go-ahead and moving them from Bermuda.
Note that Milne had over two weeks to plan and prepare in the certain knowledge war was coming, which is on top of having been planning since mid-November. The last ship he takes with him, Aboukir, only arrived the previous day, but it's him deciding to move quickly precisely so that he can throw off the Union's timetable. (Note that I specifically
exclude the
Terror, which could probably have done the job by herself.)
Also, it's not seven weeks - it's actually twelve. (7 Nov 1861 - 29 Jan 1862 is 83 days.) For it to be seven weeks from 29 Jan 1862 the incident would have to be 11 Dec 1861, which is two weeks after the news arrived in Britain!
Your picture of the Crimean War is quite unusual as war had not been declared at that point; indeed, Sinope was not for several months. April to June is also between one and three months, so at the most it's one week longer and on average should be a couple of weeks shorter. In any case, deploying as allies for the first time in decades is different from deploying unilaterally for the third time in one decade, and the British had a large fleet already on station in American waters.
It's not clear the British are going to intervene until the marked PoD, or a few days after - you may note that the US Navy
is recalled from blockade stations, but the dispatch vessel sent to the Gulf is intercepted. The US Navy in the southern part of the Eastern Seaboard recalls to Port Royal and then sails north, however this change in posture takes significant time to recall all the blockaders. Some of them go out to sea, others escort the troops back from Port Royal. Many of the modern ships make it to NY.
As for whether the USN would send out raiders or not, I was not sure of the USN's actions. Either way, it would not substantially alter the events of the coastal attacks (apart from making them easier) if the USN's ships went out raiding, and the important convoys were all well defended - usually with a frigate or corvette.
As an aside, I find it quite amazing you criticize the British taking only twelve weeks to go from incident to action, while by this standard the US Navy shouldn't be reacting until mid-April!
Please cite the timing of the arrival of these arms orders from Europe - not just conjecture, but actual timing. It's worth noting that the Federal Army had no spare weapons to give in December 1861 (instructing no more regiments were to be raised until asked for) while the Federal Army in June 1862 had 300,000 weapons spare; this indicates substantially over 300,000 of the ~600,000 weapons ordered arrived between December 1861 and June 1862. We also know that the British deliveries (to name but one) were almost entirely in 1862:
For more information I suggest the essay by robcraufurd:
http://67thtigers.blogspot.co.uk/2016/06/guest-post-rifles-trade-and-blockade_21.html
That's what they
do in this TL. They shut down all offensive operations and divert troops to the northern frontier and to the eastern ports. This is why the British don't actually invade and destroy e.g. DuPont's powder mills, but it also means that offensives of early 1862 simply do not take place. This is a diversion of roughly 150,000 troops and everyone in training!
As for strengthening the defences, they also do this - in many cases I essentially grant the Union weapons they simply did not have OTL (e.g. fort guns). Boston OTL was defended by one condemned gun, but TTL they're fully stocked - the guns have to come from somewhere, but here I assume they were just found without harming the Union war effort elsewhere.
If you look back over the TL, you will see that I had the British ironclads transit up at the time of breakup on the St Lawrence - I know the place was frozen over.
As for the mention of the Eads gunboats, you are doubtless aware that a gunboat taking from August 1861 to Feb 1862 ordered at the time of the PoD would not be completing until June 1862. (The same applies to the 90 day gunboats - since no orders took place OTL, no orders take place in advance of the PoD and the 90-day gunboats would be completing early April at the earliest, and indeed unarmoured gunboats are shown on the Lakes. They're just defeated by the British ironclads.)
If you mean that the US would go on the offensive in the west of Canada, while this is somewhat plausible it would mean the US would be beginning their preparations at (or after) the PoD while the British had already been planning defence and training troops for a month and a half. It's possible some small success could have resulted, but TTL I've had them instead focus on defence for the simple reason they can't find the troops for an offensive in the west - they've had to remove approximately 150,000 men from the southern frontier just to hold a defensive on the eastern coast and northern frontier, with no weapons to increase their numbers, and as such to allocate the troops to attack in the west they'd need to strip somewhere important of defences. (Well, somewhere
else important.)
But the Confederacy being beaten 'after March 1862' assumes the Union offensives of early 1862 happen. You earlier noted that the Union would not be going on the offensive in early 1862 and I concurred; thus I'm not sure why you suddenly have them happening again. As a consequence your point about Missouri and Kentucky - as well as New Mexico - is invalid.
As for political support for Lincoln, OTL the threat of war with Britain resulted in a run on the banks. You'll note that I've had nobody complaining about Lincoln's actions except for a noted Confederate sympathizer!
There's a reason that I had the Confederate armies - swollen considerably by absorbing troops formerly defending the CSA's coast - attack where I did. OTL the turnpike road was masked from any defending forts until one was built there to protect it well after the PoD - thus the Confederates largely bypass the fort ring. (It's a ring of forts, not a single continuous one, and as such has gaps in it - the Confederacy found one of the gaps.)
The Army of the Potomac is not in a fit state to intervene as it has fought several battles against the Confederacy, but the poor state of their weapons (see above about one third of the troops not having weapons able to be used well in the field; this is not corrected as it was OTL) and their numbers problem spell defeat. McClellan has another attempt at interfering but this also does not work; since then he's been trying to rebuild the Army of the Potomac to the point it can actually fight, and that's taken us up to the end of May.
So...
Some of these are cogent points, but in many cases I've already addressed them in the TL. Others assume things which are not the case either TTL or OTL, or seem to ignore the OTL British reaction to Trent (and the lack on the part of the Union).
I'm also extremely disappointed you didn't highlight one as your strongest, despite my repeated requests - I'm sure you'll pick whichever one you felt was insufficiently countered and call that your strongest retroactively, which is rather bad form.
In any case, I hope I've addressed most of these. Our biggest point of lack of agreement is probably the shoulder arm issue, and on that I'm confident I have the right of it - the combination of the Union asking for no more troops in Dec 1861 and the Union having something like 300,000 spare shoulder arms in early 1862 (with about 100,000 or more issued in the intervening six months) seems conclusive to me.