RE: cg dilemma
First yes the airplane should balance the same either way. The problem arises and what you experiancing when you turned it back up is there is not enought stability to be able to balance it. In other words the vertical center of gravity needs to be sufficiently lower than the balance supports to be able to balance the airplane. Trying to balance many low wings upright is next to impossible to do accurately, Just like trying to balance a pencil on its point.
If the low wing has considerable dihedral then it may be possible to balance upright if the supports are fairly wide apart. However most commercial balancing devices won,t spread that far.
If the airplane is perfectly level upside down at the point you are looking for then that is the balance point.
John