I think you are on the right track but I'm not sure I understand what you mean by a "foot" for the bottom of the garage door. This solution that comes to mind for me is what's found at the base of every underground parking garage door. Normally, there is no projection and inch higher than the surrounding pavement. Instead, there is a trench at least 6 inches and often 1 foot wide, across the entire width of the opening. The bottom of this trench is flat, or slopes slightly to the center or one side. The drain itself is not in the bottom of the trench. It drains off the side of the trench, using an elbow to reach below the water line. This approach prevents the sludge at the bottom of the trench from clogging the drains, and prevents the floating material from doing the same. There still is the potential for freezing, however that potential exists with virtually every drain. Adding some deicer to the trench during critical parts of the winter can solve this. Obviously any deicer used should be concrete friendly.