Dear @Braden Kohary,
Thank you for posting your question in the Microsoft Q&A forum.
Based on your description, the user is experiencing synchronization problems with Outlook 365 for an Exchange Online In-Place Archive. Both the Outlook desktop client and Outlook on the web show thousands of entries labeled “Modification Resolution” in the Sync Issues folders. The error details include Table critical stop property: 0x0E12000D and messages such as “Conflict generated, remote item is winner.” The archive contains more than 9,000 affected items, and the customer needs guidance on how to recover and stabilize the archive. Please correct me if I misunderstand your point.
Firstly, you should disable any processes or actions, turn off notification that are generating errors related to Table critical stop property: 0x0E12000D. After that, verify synchronization consistency between Outlook on the web (OWA) and the Outlook desktop client (New Outlook app).
In the meantime, after researching, here is information may be helpful to you that you can refer
https://library.shu.edu/techsupport/outlooklogs
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and more information from Microsoft article Synchronization log error / Modification Resolution
I hope information above can be helpful to you, if you have any other questions, please feel free to reach out.
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