Squeaking out of the rear pipes - yipes!

Sounds to me like the back pressure when you let off the gas is causing some sort of tension release which is causing something to come loose and squeak.

My guess is just as theirs, check the hangers, see if the rubber on any of them squeaks when moved around by hand. Also check the sleeving if you didn't weld the exhaust together. Maybe the clamps are just loose enough to allow it to slip around when every thing's just right.

Those are my guesses. Shake the exhaust around by hand, see what happens. Wiggle it side to side, front to back.. by the description it honestly does sound like somethings just ever so slightly loose.