WebRTC 408 Timeouts during WFM Schedule Publish for High-Volume Queues

Stuck on a recurring issue where the WebRTC softphone handshake fails with a 408 Request Timeout when the WFM module attempts to publish schedules for queues exceeding 500 agents. The environment is Genesys Cloud 2024.4 (US-East-1) with a custom BYOC edge, and the failure correlates directly with the shift swap validation batch size. Could someone explain why the media server drops these connections specifically during the Chicago morning rush (America/Chicago)?