On the supply air side, the air handling system should be designed for very low velocity to minimize turbulence, which is what creates noise in ductwork also using long-radius elbows and lining return ducts to attenuate any residual noise.”
Sound traps, which are special sections of ductwork that have very thick internal sound attenuating baffles provide a lot of attenuation in a very short distance of duct.
If you design the sound traps, specially shaped and custom built, so that they could be conveniently installed in the existing structure that would expedite the problem.
If the air handler fan motors are equipped with variable frequency drives such that only enough air is distributed to meet the cooling load then this feature not only contributes to low noise, but also saves considerable energy.