So because you have no trust at all in the abilities of your direct superiors you want to mail the big boss?

Depends on him and your superiors, but generally it's a very bad idea. You always go through your direct superior first.

If your idea is "lost in the layers" you can still cut through the layers, if you really must.

Going to the big boss directly will probably result in two things: he will dismiss it without a second thought. And your direct superior will not be happy.

And btw, six or seven figures are nice, but that's not automatically a good idea, even if your estimate was correct.