Out of curiosity I just put my Alpha RTF on the GP CG Machine and it is showing tail heavy also. This plane flies great the way it is and is the same as it came out of the box (no extra glue or balsa).
I don't know how much it would take to make it level but it would be a lot of weight as the tail easily drops to the ground when on the machine.
The plane does balance at 3 3/16 inches if that helps.