Most American conservatives of previous generations distrusted the idea that we could or should remake other countries in our own image. They shunned crusades abroad. But being American, they couldn't be wholly Hobbesian, and sovereignty-oriented in their thinking, and had to recognize standards above the merely materialist.
I'm not so sure that Burke's thought "inspired the Congress of Vienna and thus laid the foundations for what remains the world's longest golden age of peace, progress, and the advance of liberty," though. Burke may have been an important figure, but the Continental Europeans had their own thinkers and theorists, and their own agenda.
It's doubtful that Alexander, Hardenburg, Metternich, or Talleyrand imagined creating a liberal capitalist order. The international stability that they created may have helped produce such a world, but they themselves may have been more Hobbesian than anything else when they put "legitimacy" above other considerations.
I like to think of it as providing them with the opportunity to have a government like ours. That's what we're doing in Iraq and Afghanistan, giving them a shot. Weather or not we will be successful...only time will tell.