I see your point, but why is pairing 1 vs. 2 so absurd?

Becuase there are other pairings that work.

The GM's get to eat fish for one more round before agreeing to a draw in the
last round after 1. a4 a5 2. h4 h5 1/2-1/2.

You're making this hard because your starting from the bottom and working up.
You should start from the top and work down.