Line 448 and 632 from your log tells the game version 3.16. Before that I saw COM3D2.5.GearMenuFix.Patch.dll which is installed by CMI only on version 3.xx.
After some research, I think I discovered my problem. When I was updating the DLC I was unsure of which files I was supposed to be running, and attempted to install some of the files for version 2.5. The guide makes it clear that it isn't needed to update the files for CM3D2, but it was not immediately clear that I needed to update *only* the version of the game I would be using.
I performed a destructive reinstall with "I want nothing!" from CMI, then I reinstalled it as directed by the guide. After dumping the difference module and Eng translation files back into the game files and overwriting, the game started up with no issues in the log at startup. Horray, and thank you!