Official seat sales are confined to a limited period, and availabiltiy goes fast. Your best bet is to contact a Chinese "ethic" travel agency in NYC that can get you consolidator tickets at much better prices than you'll find at "traditional" sites. These are reliable sources, though you might not get mileage. You might also try connecting at another Asian hub, en route to HKG for lower fares. Otherwise, wait until CX puts its special/giveaway fares via the HKG Tourism Bureau.

The real question is what you consider "cheap" and are willing to pay? Also, are you planning to return to the US, or returning back? [Your luggage question suggests you might be concluding your studies.]