I am thinking of a "junktion" box between your cbg and amp. The box has a 2 prong outlet in it, one set of wires lead to a 1/4 jack and the other to the plug. Then, you can plug in your amp to the box, or pedal and then just use a 2 prong cord between cbg and amp. You would have to make your own custom 2 prong plug cords at both ends. But you can swipe them off of anything and the outlets would be cheap too. I just bought one at a local second hand store for 25 cents.
without a "coaxial" plug and cord you will get radio interference. this was a problem with my Grandfathers rig from the '30's he made his own jacks since it was in the Depression.