How to pause throttling and blocking of out-of-date on-premises Exchange Servers

Thanks for the response KevinShaughnessy.

For KSchneider42 (or anyone else that may be following along):

I finally got my support ticket escalated and, while I never really got an explanation of why the issue started so suddenly after years of running smoothly, I was directed to this support page:

https://learn.microsoft.com/en-us/exchange/troubleshoot/mailflow/email-stuck-queues

After modifying MaxPerDomainOutboundConnections and MessageRetryInterval to the suggested values, my connection issues instantly disappeared and have yet to return (knock on wood). Note that I did not modify the SmtpConnectorQueueMessageCountThresholdForConcurrentConnections setting in the Edgetransport.exe.config file.