I don't feed much cooked meat to my muds either. That is something that they can get too much of in a hurry.
But I do feed them cooked shrimp or chicken (small amounts!)about once a week or so. I will also shave the soft bone of the knuckle part of a chicken thigh for them too. They really seem to go nuts for this and I don't worry about them getting splinters since this 'spongy' bone.