J Campbell, that little rotating piece is called a "cam." Increasing the size, or the ramping of a brake cam will change how powerfully, and how quickly your brakes engage, respectively.
So far, that's a good plan, but putting an unsecured piece of metal inside your brake drums is a Very Bad Idea. Even if you shim your brake cam to get better performance out of it (and somehow avoid over-shimming so as not to burst or crack your hub) you can't just leave that shim there - you need to do _something_ to secure it in place.
The perfect implementation of your plan would be to remove the cam, weld on some extra metal, and then file it down until it is exactly the right shape to engage the shoes on the inside of the hub shell.
At the very least, use some glue, or a tapped-and-faced hole, or a flattened-thimble-like covering that bolts to the flat side of the cam, or...
Increasing the length of the lever arm on the brake hub itself will make your hand lever move more (you'll have to pull it farther, and have less adjustment room) to make your brake shoes move a shorter distance more powerfully.
Colin, if your brakes are in good tune, and you haul on the hand lever without bottoming out at the handle bar this would give you more braking power (and probably better braking response).
Brake drum lever arm failures are among the primary reasons old motorbikes were recalled. I'd suggest finding a bigger lever arm, or building an entirely new, larger lever arm (basically, don't try bolting on an extension to the existing arm).
Do we just assume that Colin knows to de-glaze the insides of his hubs? Colin, do you know to de-glaze the inside of your hubs?
As brake shoes wear, they leave a burnt deposit on the inside of the hub shell (they shouldn't, but they do). Brake cleaner gets this off, as does sandpaper. You are not supposed to use sandpaper for some reason (asbestos? Brake surface scratches? I don't remember).
Doesn't the Sachs use a coaster brake? Coaster brakes have a sprocket with a threaded cone. When the sprocket is rotated backwards - when you pedal backwards - the cone "unscrews" from a pair of brake shoes inside the hub - in effect, the sprocket replaces the brake cam as the actuating method.
I think that this means that you can roll a Sachs with a coaster brake backwards without the pedals turning. I am not sure how useful that would be.