Mike,
Good observation... my question to you is, do you keep the lid on the LBE all the time except when adding/removing the pizza? The 2stone model I have is open in the front and not put on the grill with a lid, so if you keep the lid on, that would probably help explain the bottom burning more easily. The bottom stone of the 2stone also rotates, which probably helps a little, I imagine.
~mots aka sd