You're right on some points. The US regime right now is hoping they can co-opt Russia to make them an ally against China. The irony is, I had the same idea five years ago. And back then, it could have worked. But the barbarism Russia inflicted during the invasion of Ukraine made the idea of an alliance with Russia anathema.
As for whether China or Russia is a "more valuable goal," I think this misses the point. Russia, China, and Iran (and their vassals Belarus, North Korea and Hamas) are an axis. We don't have the luxury of choosing which one to fight. They're all working together and have to all be taken down. Is China the most powerful of that axis? Yes. Is China the leader of that axis? Yes. But the entire alliance has to be crushed.