NavalDesign,
Sorry, I was addressing the original question, not your reply.
I agree that the trapezoidal tank will have a clear change in LCB as the VCB rises, but as I said in my previous post, if the vessel has any trim there is also a subtle shift in LCB when you raise the VCG in a completely parallel box shaped tank. There is also a longitudinal shift in the fluid in a half full tank with trim that does not occur in a full tank with a fluid that is half as dense.
The combination of these two factors can result in small differences to the LCB and therefore bending moment, however this difference should be extremely small in most cases.