I figured out how to do this.
When you upload image.jpg for the TwentyTen header, WordPress creates a cropped version of the header image, calls it cropped-image.jpg and saves it in wp-content/uploads.
All I had to do was find the cropped-image.jpg file in cPanel and replace it with the the 1880 x 396 version. Now it works perfectly. WordPress calls up cropped-image.jpg, scales it down to 940 x 198, and displays it on the header, but because it’s @2x the size, it looks perfect on Retina displays.