Hm interesting thought. However, if you are flying out on SQ1, it's fairly difficult to say when "exactly" you will cross the IDL because of the varying weather conditions and prevailing winds. Like for example, once when I took UA from SFO to HKG, the airmap showed that the flight went straight over the Pacific, while another time I was on SQ1, the plane went up through Alaska, over Mongolia, and down through the Malay peninsula.

You may be able to research the flight patterns for the past week, but other than sitting in the plane and figuring it out, it's difficult to pin an exact time.