Realistic ways in which Alaska ends up British, thus Canadian, and not American?

  That was one of the factual errors.  Along with things like the US taking over Texas in 1836 IIRC and a couple of others.  I think after the defeat in the Crimean war the emperor realised he needed resources to upgrade both his army and also infrastructure.  For instance in the winter Russian forces/supplies were being sent to the front by sledge and hence took longer than it took British forces to reach there from Britain.  Also that, with the collapse of the fur trade it was an isolated outpost a hell of a way from the Russian centre of power and as such a drain on resources.