All,
Thank you for all the thoughts and insight - it is much appreciated. To answer a couple of the questions raised in the responses above:
1. I did feed the ammunition through the magazine (not dropped into the chamber singly). I haven't posted this problem on any of the other gun boards.
2. As Der Ami suggested, I did wonder whether the 6.5x54 rifle was chambered in the 6.5x54 Mauser cartridge, instead of the 6.5x54 MS cartridge, given that the rifle is a Mauser. The seller had the rifle listed as a 6.5x54 MS. I did peruse the nitroexpress forum, and it was stated that the bolt would not close if a person attempted to chamber a 6.5x54 MS in a 6.5x54 Mauser chamber (
http://forums.gunboards.com/showthread.php?332929-Pre-war-mauser-oberndorf-model-98-type-m-6-5-x-54). The 6.5x54 MS round did chamber just fine, but I will go back and measure the fired brass. I was able to chamber and extract the 6.5x54 MS round with no issue when I shot the rifle.
Below are the photos of the "other" (6.5) rifle's proof marks:



My plan is now to make cerrosafe casts of both chambers. I'm going to redo the 7x57 to confirm what I got the first time. I'll post back with the results. I'm also going to measure all the various 7x57 commercial rounds I have on-hand to see how they compare. Thanks again for the help.