So in this situation, we don't need to look at the tidal gravity over the length of the 200 km chunk, but rather on the tidal gravity between this chunk (its center of mass) and the center of the Earth since it is still attached to the Earth. right ?
Well, we found a method to determine if something breaks up at all. That is the 6.5 to 6370 km comparison, and indeed 6.5 < 6370. If it breaks, where does it break? That is a complicated thing, probably in the middle for a completely homogeneous material. It breaks there before we reach the point we considered. For the smaller chunks, we can ask the same question again. Technically, we would need to modify the gravitational forces, because suddenly some part of Earth is not there any more (or at least in some distance). But we can find an estimate for the largest object that can support its structural integrity for a given tidal acceleration. That's the 200 kilometers, as order of magnitude estimate.