Don't bother with non-Lance/Glaive/Bow/Hammer Grids. By replacing an Assault weapon with something non-Assault like Phantom Axe, you lose about as much damage output as you gain from the base Atk. So, the upgrade is very minimal. Is it better than a non-Phantom Grid? Yes. Barely, but yes.
Is it worth your time, effort and resources? No.