Control of an unsymmetrical quadcopter

I am currently developing a quadcopter with an attached arm. The arm is effectively a long rod which is attached at its midpoint (which is also its center of gravity) to a gimbal mounted above the center of gravity of the drone.

I expect that when the pitch of the arm differs significantly from that of the drone, then the body-aligned moment of inertia tensor for the system will contain off-diagonal terms. As a result, a coupling will exist between the torques applied about the drone’s body frame axes, i.e. a roll command will also produce torques about the pitch and yaw axes.

Does anyone here have any experience or suggestions regarding how to handle this issue? I am currently looking into replacing PX4’s rate controller module, but I am not sure that this is the simplest route to solving the problem.

Thanks.