Advanced cPanel Server Management: Handling Resource Spikes?

Our 'Website Maintenance & cPanel Management Services' team is currently grappling with a persistent and complex issue for one of our high-traffic clients. Despite deploying robust hardware and implementing initial, comprehensive optimizations, we're encountering intermittent service degradation during unpredictable traffic surges. This isn't a straightforward case of server overload where physical CPU, RAM, or I/O limits are being hit; rather, the bottleneck manifests specifically in Apache/LiteSpeed process management and PHP-FPM worker saturation, leading to application-level timeouts and extensive process queueing.

For instance, during these spikes, we observe patterns like the following in our logs:

[Mon Apr 08 10:30:15.123456 2024] [mpm_event:error] [pid 12345:tid 1234567890] AH00487: server reached MaxRequestWorkers setting, consider raising the MaxRequestWorkers setting
[Mon Apr 08 10:30:15.123500 2024] [proxy_fcgi:error] [pid 12345:tid 1234567890] (70007)The timeout specified has expired: [client 192.168.1.1:12345] AH01075: Error dispatching request to : , referer: https://clientdomain.com/
[08-Apr-2024 10:30:16] WARNING: [pool clientdomain] server reached pm.max_children setting (100), consider raising it
[08-Apr-2024 10:30:17] WARNING: [pool clientdomain] server reached pm.max_children setting (100), consider raising it

We've already gone through the conventional playbook: meticulously fine-tuning Apache's MaxClients/MaxRequestWorkers, adjusting PHP-FPM pool settings (pm.max_children, pm.start_servers, pm.min_spare_servers, pm.max_spare_servers), implementing and refining mod_evasive and mod_security rules, and conducting extensive MySQL optimization (buffer pools, query caching, slow query analysis). We're seeking advanced strategies beyond these conventional server management practices to proactively buffer against and recover from these sudden, massive resource spikes within a cPanel/WHM environment, without resorting to full containerization or a reverse proxy outside cPanel's direct control. What novel approaches have others found effective in similar scenarios?