But not all 2-row malts taste the same. And if you believe the origin story of California Common, it would have been using whatever grain was available during the California gold rush, which would have been 6-row barley if anything. British pale malts in general are more kilned than in other parts of the world, and Otter in particular has more character than most other barleys. So if you can't readily get US malts, I'd probably go with a standard UK pale malt (as opposed to a premium one like Otter) and make it blander by diluting it with some pilsner or extra pale.
But what is currently thought of as California Common is not really a style as such, it's really an attempt to retrofit a style onto Anchor Steam, which claims origins in 19th century California but which was reinvented when Fritz Maytag bought Anchor in the 1960s, at a time when he was significantly influenced by British beers. I've seen suggestions that the actual 19th century beers were rather different, but of course we'll never really know.
Local styles of beer in general are all about taking inspiration from favourite beers from elsewhere, but making do with local ingredients and local conditions - you see it at the moment with the 4% cask ales made with Citra etc, taking the idea of the US kegging a 6% Citra IPA and adapting it to British tastes. And California Common is a specific example of that make do and mend approach to adapting to local conditions, so in a way it's not a "style" to be "true to".