I didn't read the complete thread, but we have various WP sites online. We only encounter high cpu when there are xlmrpc.php attacks or distributed attacks.
Is there nothing to be seen from the domain logs which is causing this high load?
You know I had some issues with exit code 70 while we had way then enough memory and also enough memory put to php. This seemd to be a hardware error. Now on the new server, we only had this issue once until now. So maybe it's also caused by some kind of attack.
Anything to see maybe on the enhanced apache server status which you can call via the web browser?