To expand on the dowel - definitely worth doing but masonry style, not close fitting or you will never get it aligned as mentioned above. Drill a couple of holes in both sides fairly well aligned and use screws or pieces of wall tie as the dowels (loose in holes). Once happy it will push back into place, glue on the faces and in the holes and push it in place. If you must remove the Cill, a carbide reciprocating saw works well