To be fair, the MG13 bears no relationship to the MG34 at all, although you are correct in that it preceeded the MG34. It was developed in the early interwar years, and its lineage is from the Dreyse HMGs, and shares the same action as the Dreyse 1918.
I acquired a 1918 Dreyse watercooled HMG some years ago that had been obtained by the seller without a bolt. An MG13 bolt fit perfectly although minor modifications were necessary since the MG13 feeds from the side and the Dreyse HMG form the top, as it is belt fed.
The MG13s are very pleasant to shoot, although the 20 round mags are too small, really. They used a 75 saddle round saddle drum fitted with a feed tower, which inserted into the magwell, but the drums are virtually impossible to find. If anyone finds one and wants to sell it, I need one.