You have some good points.
I will go into the American economic problems in future chapters.
Gold should not be an issue as the control over the California, British Columbia and now Nevada gold fiels had hard currency rushing in. Probably, the loss of grain exports and lack of steel and niter imports were bigger problems.
I don't think that an invasion of California...or even an expedition to regain British Columbia was likely in the near term. The logistics were simply too far much. We are talking supply lines of 8000 to 12000 miles depending on origin of the invasion (certainly British would not use any forces from India only a few years after the Mutiny).
The undersea cable would give an advantage in communication. It would allow reinforcements to arrive without warning from Britain but whether resources to do so would be available is another question.
I don't think that the British in this scenario would be able to REACH any of the Great Plains Indian tribes.
I just did a bit of research and the trans-Atlantic cable was not completed until 1866 by a joint British-American group. Therefore I don't think it would have an effect on this TL.