Some hot rods mount the mirrors at the top of the door frame - this is much closer to the eyes and you might be able to get by with a smaller mirror in that case.
Here's an example link:
CAR FEATURE>> FJ45 LAND CRUISER LOWBOY HOT ROD - Speedhunters
Now in this case the front of the door is fairly vertical and the mirror isn't much closer to where it would be if it was mounted below the window, but on cars with a substantial windshield rake, you might be able to get it a fair bit closer than it's stock location.
Taken to the extreme, I recall mirrors for cyclists that mounted on the helmets - they were almost postage stamp sized, but because they were so close to the eyes they gave a large field of vision.