Don't forget Google Flights to search for prices, easily lets you filter by alliance, destination (can even search a region/country), date, etc.
And follow/subscribe to the Premium Fare Deals forum here. I flew a JFK-CDG-HKG r/t in AF business for ~$2,000 a couple years ago that I found there. A bit long of a routing, but got a half day in Paris on the outbound and a poop-ton of MQM/MQDs.
Lastly, consider an American Express Platinum charge card, which has the International Airline Program with often decent (10%?) discounts on published fares, works with DL/AF and probably some other SkyTeam carriers.
ETA, ok, really lastly, keep in mind that restricting yourself to SkyTeam to earn DL status will likely cost you more than going as a free agent and just searching for the lowest fares. There are limited benefits to status when flying int'l business class anyway. Basically just bonus miles and priority in the telephone queue (but only on DL).