Something I should point out is that the analysis I did, which looked at the things the Union could do to deploy more troops, flagged up quite specifically the tradeoffs involved.
I could, similarly, show that the British have soft deployment limits after which they are accepting additional risks and tradeoffs. For example, they have 25 disposable Armstrong 12 pounder foot batteries in Britain and 10 disposable Armstrong horse artillery batteries in Britain, so after that point the choice is going to be what to arm Canadian militia batteries with (or possibly using British militia batteries that have volunteered for overseas service), though in both cases if given Armstrongs they will be substantially less efficient with them than the British regulars.
I think it is likely that (in keeping with standard British corps structure) they would add one positional battery per corps. That is militia gunners armed with 20 pounder Armstrong guns, which would not manoeuvre with any detached forces but would accompany the corps.
Similarly, for the British to expand their field strength in Canada and the Maritimes beyond 66 battalions of infantry and 15 regiments of regular cavalry means using Canadian troops. This augments the size but lowers the average quality of the British field forces.
Tradeoffs are not absent for using Canadian troops either and the supply is not unlimited.
In Canada proper there are, attested, 1 oversized battalion of regular infantry (that's the Royal Canadian Rifles), 193 companies volunteer infantry (incl. an Irish battalion from Montreal volunteered during the crisis), 34 troops volunteer cavalry. 8 volunteer field batteries, 7 volunteer foot/position batteries, 12 volunteer garrison batteries, 5 volunteer engineer companies and 7 volunteer naval companies. Those are effectively baked-in as available - it amounts to about 19 volunteer battalions of infantry, a non-trivial but not very large amount of volunteer cavalry, enough volunteer artillery to provide the position batteries I mentioned and the field artillery to accompany the infantry, and some miscellaneous garrison and engineering companies. Effectively there is more than a division of volunteer Canadians, though less than two. (I did not account for volunteer Maritimes support here).
The majority of Canadian manpower contribution would be their militia. The first planned Sedentary militia callout (of 46 battalions in Canada proper, plus - to my recollection - 7 in the Maritimes) was expected to be fully subscribed or oversubscribed, meaning that it would generate another 46 battalions in Canada, raising the expected Canadian manpower to about 64 battalions - on par with the maximum British commitment. Some of this militia callout may end up diverted to artillery roles as there was quite a lot of artillery in Canada (by no means an unlimited amount, but enough to fit the expectations of the defence scheme's requirements for batteries in various places).
A second militia callout is much less likely to be fully subscribed, as it starts to tap out Canadian mobilizable manpower, but it would certainly generate a lot more than nothing. The first callout was one company per battalion of the sedentary militia.
Arming these Canadian troops would in many cases initially be with percussion muskets, though large numbers of Enfield rifles were sent both during and after the crisis and so by the time of the thaw they would mostly be equipped with Enfields. The initial bottleneck on Enfield numbers may complicate rifle training, though.
All of these things and the tradeoffs involved with them are baked into the assessment of the British and Canadian position. No posters that I am aware of have been presenting a British or Canadian position that is more rosy than they can substantiate with evidence (certainly I can name every single individual British infantry battalion, cavalry regiment, field battery and Canadian volunteer formation I have just enumerated).
Bringing the