"When GW1 ended, Resolution 687 recognized the cessation of hostilities.

This means that in no way can resolution 678 be used to justify GW2. 687 put an end to 678."

In your dreams. "recognized the cessation of hostilities" is simply stating that- both sides have agreed to stop combat operations. The war hasn't ended- you have numerous conditions that need to be fulfilled. With the assumption that these conditions will be completed, you can say the war is over.

You are attempting to say that 678 was nullified which of course it was not. In law, a law passed after another law does not alter the previous law unless it specificly states it is altering it in some way or it's cancelling it. Any law remains on the books unless it is specifically altered.

As stated in the your link on 1441:
"Recalling all its previous relevant resolutions, in particular its resolutions 661 (1990) of 6 August 1990, 678 (1990) of 29 November 1990, 686 (1991) of 2 March 1991, 687 (1991) of 3 April 1991, 688 (1991) of 5 April 1991, 707 (1991) of 15 August 1991, 715 (1991) of 11 October 1991, 986 (1995) of 14 April 1995, and 1284 (1999) of 17 December 1999, and all the relevant statements of its President"

We know that 678 is still valid at the time of 1441- else, it wouldn't be "recalled" or mentioned as relevant. Now parts of 678 can be altered by later resolutions, but you are required to show the specific wording which altered it in order to say that the document or parts of it is no longer valid. And additionally regardless of what the UN Security Council it's treaty-like agreements are, technically they only become law as far as the US is concerned after our Senate has ratified it.