Okey, this is a lesson we need to teach all motorcyclists. Due to the speed bicycles run, a lot of people get away without it.
Take your current bike, and try and flip over the handlebars. Try it! Get good at it. You're admitting you lack the subtle control that you need to efectively brake with a bicycle, or even a car. (your car has a 70/30 split or worse with the brake bias)
It's a skill you should learn. :-) Get good at it. It will make you a much, much better rider. (I learned this lesson back in high school.)
Now your thought of mounting pegs to the back of the bike is a bad idea. It will give the bike a really good way of biting a hole in your calf when you fall off on a downhill. Moving your legs back like that won't make a signifigant change in the amount of weight you can get over the back of the bike. If you want to brake hard, or go down a hill, just lean back. There have been times where I've had my seat square in the middle of my chest.
You'll probally get away with this... But if you did it on a motorcycle, as a community we'd be making a pool to see when you died. Thankfully bikes are more forgiving.