increased local crystallinity
The last statement you quoted is very key, and new to me. It strongly implies in-situ formation. Replacement reactions (as Nick mentions) could account for this. Consider Chert nodules, often found in limestones or chalk deposits. Their mineralogy is completely different from the matrix, and they generally have no internal layering. Altered zones ("areoles" ??? works for me!) near nodules are often present, such as depletions or recrystalizations. Nodules are usually rounded, and only sometimes have identifiable nuclei. Earth has been too wet to have any extensive sulfate deposits, but perhaps hematite nodule formation is likely under such conditions.