3D Localization/Registration/Reconstruction are traditional area of use for regularized Gauss-Newton and all are highly non-convex. The trick is to strat in nearly-convex area, sometimes after several tries, and/or convexify with regularizers and/or sensors fusion.

K-FAC seems stable enough but quite complex in implementation. It's identical to low-dimentional-blocks approximation of Gauss-Newton. Fisher information is only decoration.