Given your criteria of length, alpine terrain, and few people, I'd say doing a long section of the Continental Divide Trail (the 'CDT' mentioned already) probably fits the bill about as well as anything out there. It may not be all alpine or entirely empty of people, but it has enough reality you won't need to invent it, and it is long enough, wild enough, alpine enough and parts of it are lightly-used enough that you should be able to identify a section that you'll enjoy hiking. If you are looking for a challenge, you can find it there.