Apparently, a missing crescent moon and crown is not unheard of. See this link for a discussion:viewtopic.php?t=6048
If your mark has K J pierced by an arrow from left to right, we are probably talking about the same trademark. Kollmar and Jourdan registered this mark in the United States in 1964 for (1) watch casings and parts thereof, and (2) Jewelry and ornamental objects for personal use, made in whole or in part of gold or silver . . . . The TESS [Trademark Electronic Search System] listing states the mark was first used in 1910, commercially in 1925, in both categories.
I hope this information is useful to you. Kit