Fix the problem, not the dog
Let's resolve this issue another way: some drills to learn how to use your front brake. If you get your weight far enough back, you can use only your front brake to stop or slow on all but the steepest of hills, and here's how you're gonna learn to do it:
1. Go to a grass sports field it's cool to ride on. Practice stopping from some decent speed with Only the Front Brake. Start with mellow stops, if need be, and move your weight back a little. Brake harder and harder...try to skid the front tire, but compensate by getting your weight back so you don't come up off the ground.
2. After you've gone nuts with hardcore, super hard front braking that didn't cause you to cartwheel like our Mom's would say would happen, you'll have felt the forces wanting to lift you into a nose wheelie. Now, do more braking, but do it so you DO nose wheelie, and then use a slight (this is feathering) release on lever pressure to drop yourself out of the wheelie. Also, since you're on grass: do it so you do flip a few times.
3. Go ride a trail, not including the descent you pitched on, and use only your front brake for the ride.
4. You're done. The next time you ride, you'll have front-braking down pat, and can use the brakes together on any slope. When you start to over-brake, you'll just ease off, just like on the grass.