i listened to the sound, even though it sounded muffled... you were driving, at a slow speed, (about 30-40 MPH?), and had this sound... did the sound come from the front, back, left or right? i assume you had your windows down when you recorded the sound... the frequency of the beat sound as if something stuck to a tire and beats on the road as thhe tire is rotating, as the timing between each beat as if it is approximately the time for a tire to make a full rotation. once the speed of the car increases, the beats happened more often, as tire rotates faster, and to a human ear the beats blend into one, solid humming noise... I do not suspect the engine components as the rotational speed of the engine is much faster in hundres of rotations per second... not to discount the possibility of a beating timing chain but I don't know if the timing chain is prone to failure on the I-6 engines...
you mentioned that you changed brakes - was everything secured properly? you say tires were replaced but since there is no vibration, it is probably not a flat spot on the tire... another thing could be, a balancing weight on a wheel is rubbing against the brake assembly...

drive by a wall (like a sound wall on a highway), with window open, and listen to the sound.. try to drive fast, and slow, to see of the rotational frequency coinsides with the speed of the car, while driving slow and listening to the noise, rev the engine in neutral, to see if the noise will pick up or stay the same - if it picks up with the engine, something in the engine, if stays the same with the spedd of the car, then it is in the tires/wheels/brakes...