Travel websites quoting cheaper rates than travel agencies is a rarity, especially for International travel. From my own experience, skyscanner.net and cheapoair are two of the best. 

You could simultaneously try purchasing your tickets via travel websites (make sure you've cleared your browsing history/cache,though) and travel agencies. I purchased mine via AeroNepal and their price was $40 cheaper than what I was quoted on cheapoair. 

Since you've got all the time in the world prior to your departure, you could try calling/emailing various travel agents.