I've got my Mojo 40 balanced at 6 inches back and it's definitely not tail heavy.I’ve triple checked the cg, it’s tail heavy and probably needs about 8 ozs. of nose weight to get the cg it at 4-1/4”.
Short answer: No.Since I have up elevator trim for level upright flight, when inverted wouldn’t it make the nose pitch down?
The excess up elevator trim is the result of a nose heavy plane and made even worse by adding down thrust. The stab and elevator are needing to create a downward aerodynamic force in order to keep the nose from falling.
Once the plane is inverted the nose heavy condition is also trying to drop the nose. The stab and elevator are still creating the same aerodynamic downward force to pull the tail section toward the tailwheel. But now this force is acting to lower the nose even faster.
On a 3D plane that's correctly balanced, the aerodynamic force of the stab and elevator will be close to zero. With the correct CG the plane won't try to dive or climb in hands off upright or inverted level flight, so the stab and elevator don't need to produce any aerodynamic lift to raise or lower the nose.