I flew to AMS last year on Dec 28th. It was significantly cheaper to fly YYZ-LGA (1 ticket), JFK-LHR (2 ticket) and LHR-AMS (3 ticket). Total was about $600 CDN.

If you don't mind changing airports, and getting extra miles, then consider that option. Usually a break at LHR always reduces the price and UA was having a sale JFK-LHR return for $300 CDN, all in.

FYI, these tickets were not booked until October.