Hello, @Matthew Turney,
Welcome to the Microsoft Q&A platform!
Notice that you have taken steps to ensure that TLS 1.2 is enabled and being used but the issue still exists. I would suggest you try the following to try and resolve the issue:
1.Check for Updates: Ensure that your Exchange Server and Windows Server are fully up-to-date with the latest updates and patches. Older versions can sometimes cause issues with the Hybrid Configuration Wizard (HCW) and Federation Trust.
2.Check Hybrid Configuration Wizard Logs: The HCW logs can provide more detailed information about where the process is failing. You can find these logs at "C:\Users<YourUsername>\AppData\Roaming\Microsoft\Exchange Hybrid Configuration" on the machine where you ran the HCW.
3.Check Firewall and Proxy Settings: Make sure that there are no firewall or proxy rules blocking the traffic between your Exchange server and the Office 365 endpoints. This can sometimes cause unexpected connection drops.
4.Service and Account Permissions: Verify that the account you are using has the necessary permissions to perform the Hybrid Configuration.
5.Testing Connectivity: Use tools like "Test-FederationTrust" and "Test-OAuthConnectivity" PowerShell cmdlets to test your federation trust and OAuth configuration. This can sometimes reveal more specific problems.
6.Re-run HCW as Administrator: Check again that you are running the HCW with administrative privileges.
What I have provided above is a routine troubleshooting for researching such issues. If your problem is still not solved, here is a document that can help you, based on the error information you provided, please focus on error 3 and its solution, hopefully this will help solve your problem.
(Document Link: https://techcommunity.microsoft.com/blog/exchange/how-to-address-federation-trust-issues-in-hybrid-configuration-wizard-hcw/1144285)
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Thank you for your support and understanding.
Best Wishes,
Alex Zhang