I would try designing a Pega Email Channel (usign App Studio) that instantly saves incoming messages into a background waiting line rather than processing them all at once. This setup utilizes an automated Email Listener to pull the emails from your server in safe, manageable batches. Queue Processors then divide and conquer the workload across multiple server nodes, automatically turning the emails into cases without slowing down your system. The cases can be also routed intelligently.
As an example, in this article, I created an email channel to process an incoming email to create a case - How to use Pega GenAI Connect to process incoming email and attached document