Hi -DSH-. I am not sure there is an appropriate place. In my small experience, most of the requests for flying a particular route in a small range of dates are answered by a recommendation to speak with a travel agent.

My only suggestion for ways to search would be to use the ITA tool and leave the "check seat availability" option un-checked. This should give you the ability to see the lowest fares available in the market. To be honest, I have never been able to find things that are very well-priced in late December and the first few days of January. And a $3500 business class ticket on AMS/NRT does not seem too far out of line for me, even before the stop in SIN or HKG. The natural candidates for such a routing (SQ and CX) have prices that are waaaaay out of the range.

You might also consider hopping a quick flight to London and checking out something like LHR-HKG (through a consolidator, perhaps?).

I don't think you're dealing with a real easy request, to be honest.