Ok, too much, huh? That's me ... however, regardless of CPU's and time settings etc. you need to ask provider about the mod_security errors.
Both of your logs shared show this:
Execution error - PCRE limits exceeded (-8):
coming from your own host.
[uri "/courses/theme/yui_combo.php"]
that's your themes ... any and all that use yui_combo.php
Get that sorted and might not have to increase php times at all. Check with provider about it. Do you have the ability to turn off mod_security?
Just my 2 cents!
'SoS', Ken