Brad, you are going to have to make two adjustments to your image in order to get good printing results. First, is to make your image the correct aspect ratio. As you have already determined, this process will result in some cropping of the image. That's just the way it is and it will never change; crop to 8x10 and be happy.
The other adjustment you need to make is to set the resolution of your image at the same resolution as the printer. For instance, if you are printing at 300dpi (dots-per-inch) you will need to make your picture 2400x3000 pixels in order to print 8x10. Now, your printer at home can automatically resize on the fly, but you are best served by doing it yourself ahead of time in PhotoShop.
As a bonus, if you are going to print at a Costco, or other quality printer, you probably can find a printer profile at
www.drycreekphoto.com. This will allow you to preview the picture using a printer profile that is loaded into PhotoShop. You then can make adjustments to compensate for the brightness and reflectivity of the paper that they printer uses.
Good luck!