France and French Guyana?
If you just need water East and West Malaysia or Indonesia also work
Again, units that are demographically similar. Guyana is dominated by their homeland just as Hawai'i is dominated by the US.
Indonesia is an island chain, as is Japan for that matter, and both are relatively contiguous.
Malaysia may be the best exception to the rule, even though Sarawak and Sabah combined have only 1/5 of the total population of the nation. The rest is concentrated in Malaya proper. That, and I think that Sarawak is relatively autonomous as it is, if I remember correctly. Even then, they are geographically close.
To speak strictly to the OP's question: even if the British Empire included all of what would be today's United States and Canada, they would not be able to rule the world. If only for the simple reason that holding down such a vast empire would take immense resources and effort to coordinate before the age of modern communications.
There's also the issue that Britain's likely rivals (France and Russia) would certainly adjust their geo-strategic aims accordingly to counter the threat of such a super power.
This also ignores the issue of how one would over time coordinate the vastly different priorities and problems inherent in ruling a large maritime empire versus a continental one.
Pretty much this, in the end. to keep the union together, there would probably be a devolution of powers. I'm almost imagining a split like in Castille/Aragon, where one nation is responsible for one part of foreign adventures, while the other half is relatively insular and focuses its attention elsewhere.
Now, here's a question: If a sizable portion of the British Empire remains directly connected (For argument's sake, let's say the UK, this North American Union, a South Africa Analogue, and Australia) if loosely, does the capital change? Remain in London? Start rotating between cities?
I don't think we'd get to 2Georges level of Britwank by far, but the possibility for something lesser is there.