Unfortunately, nothing else about the plane is "symmetrical." For instance, there are prop P-factor, down- and up-wash, engine torque, and gyroscopic precession from flying the plane around the flight circle as well as in maneuvers. I don't think that you can get gear drag to balance the cabin drag. My last plane is pretty symmetrical with thrust line, wing chord, and tail chord aligned together, but I did this only for comparison with a certain other plane and NOT with the intention of getting symmetrical responses. There are advantages in raising the stabilizer above the wing, some relating to these other asymmetries. Regardless of what you try, the plane will present a bundle of balances and compromises. Here's hoping that your plane comes out well and that you are able to trim for the unavoidable asymmetries that all CL planes present.
SK