Earth sandwich reference map

Belgian humorist Kamagurka wrote, "Placing two slices of bread on either side of the globe doesn't mean you got yourself an earth sandwich."
American humorist Ze Frank disagrees. His earth sandwich project includes a Google Earth-powered tool to find your antipode.
Unfortunately, this map I made shows (bright orange areas) how rarely land is found on opposite sides of the planet:

• Antarctica overlaps with Greenland, Northern Canada and Northern Siberia.
• The Iberian peninsula overlaps with New Zealand.
  -Argentina and Chili meet China and Mongolia.
• Peru and Venezuela are opposite South East Asia.

Not promising. Here's hoping that Ze's mission succeeds.