Had my son push the brakes as hard as he could with the engine running, and put a long bar between the studs on the hub and tried to move the entire assembly, because it's rotationally related. I also whacked the tires with a sledge hammer in all directions. Nothing.

Funny thing is, I just put Energy Suspension bushings on the front sway bar.

The key thing is, it happens ONCE when applying the brakes, until it's driven a few minutes (bumps).

And, if I stop somewhere where it's safe, and go in reverse, hit the brakes, it does it ONCE even when repeatedly doing it in reverse. Then go into drive, it does it ONCE. Go back into reverse, it does it ONCE. Back to drive? Does it again - ONCE.

If it was sway bar end-links, it would do it every time.

It's not driveshaft or otherwise driveline related, it only happens when applying the BRAKES. And it takes a moderate amount of pedal pressure to make it do it.

I do not feel anything in the brake pedal, nor the steering wheel, I only HEAR it and feel it through the floor (chassis).

I noticed that it doesn't want to stay straight on the highway anymore. It's either left or right (like it lost castor on one wheel). Yesterday and today, it's not making the noise whatsoever, and it drives straight on the highway.

A ball joint has the ball, the socket, and an intermediate shell. I am theorizing that the shell has a worn spot and it rotates sometimes so that the castor is not effected when it's not in the right spot.