The only way to get a shorter distance than the great circle route is to tunnel through the earth. For example, the great circle route halfway around the equator is roughly 12500 miles, but the distance through the center of the earth is only 8000 miles. Of course, tunneling airplanes do not exist at present, and the great heat just a few miles down would melt one anyway!

Regarding the small extra distance involved in flying above the earth's surface, I am reminded of a problem I got in grade school: If the earth's equator is 25000 miles around, how long is a rope suspended one foot above the equator? The answer is 25000 miles plus 6.28 feet. Not much longer, in other words. A plane flying 6 miles above the equator would fly 25037.7 miles.

Bruce