Another thing on the dulcimer bridge slots is to be sure they slope down away from the vibrating portion of the string, so the string is stopped precisely at the edge of the bridge and not somewhere within the length of the slot or at the other side. Often a rattle is caused by a string vibrating in the slot itself. If your bridge fell off when the strings broke the first time, you might have reversed it so the slots slope down towards the vibrating part of the string - that could cause this problem for sure.