Flights to Japan are generally much cheaper in the winter than in the summer, sometimes 30-40% less. I'd try standard airline websites first.

If the prices you find are still too high, keep trying. You're planning an awfully long way ahead for next winter's vacation, and prices may drop overnight in the fall if the airlines aren't filling up their planes. It's always a gamble.

Another option is to try travel agents that cater to Asian immigrant communities. Flights to China or Korea often stop over at Narita.

About your timing, be aware that January 1-3 is the New Year's holiday period, which means that almost the entire country is shut down, except that the trains and planes are jam-packed. You'll still be able to see temples and shrines, but other attractions may be closed.