RE: CG location when fuel is burned
Perhaps the problem here is the assumption that the CG is a fixed point during flight. It isn't, not in models, not in full-scale.
The "optimal CG" is determined by the centre of lift (among other things) and this is the point modelers usually are trying to get their planes to balance at. We do this when the tank is empty. Thus, at take-off, our "actual CG" will be somewhat forward of the "optimal CG". As fuel is consumed, the plane will balance further aft, but it will never reach a point where the "actual CG" is behind the "optimal CG".
This is good, since having the "actual CG" too far aft leads to pitch instability.
The changing point of balance is one reason models and full-scale planes have trim adjustments.