Last time I ran into the problem you are describing was with POTS lines where the feed ran too close to an Edison Vault. As long as you were talking and the echo can had a high noise to filter out it was fine, as soon as you stopped and the noise floor leveled out it would slowly start to his sounding like an airplane.

You are having problems i've almost never seen with a T1. Closest I have seen to what you are describing are bad DSPs/Cards at the CO.