I have approached this problem two ways. One was to make an extended holder for the parting tool so it was further out from the turret. This means the turret is back far enough for the parts catcher to come up. The other was to make extensions for the parts catcher using Coroplast fastened on with small bolts. The Coroplast is rigid enough to catch the parts but if it gets caught in the chuck or turret just crumples and tears.
An open mind is a virtue...so long as all the common sense has not leaked out.