First, the Schäffer Affair goes better for the Russians, giving them a stronger base in Hawaii. Let's say they back Kaumualii in a winning bid for an independent Kauai. The Kingdom of Hawaii gets split up and devoured by Russia, Britain, France, and the US over the next 30 years or so. The Russian base in Kauai gives them a stronger position for supporting Alaska as well as for the Pacific fur trade.
The second is to delay the development of British Columbia by having the gold rushes in the area delayed by 10-20 years. That puts off the larger population.
So we have a stronger Russian Alaska and a less threatening British Columbia, resulting in less of a need for the Russians to sell Alaska, even after the Crimean disaster.
I've got some ideas where this is headed, but I want to know if it's a plausable way for Russia to keep Alaska.