Hi robbyq, I should have given more info. We did try that before I posted. When we killed Apache, neither Apache nor NginX would start. When we restarted the server, Apache restarted, but no NginX, and our test website was unreachable (Unknown Host). LeafDNS and IntoDNS both showed the DNS resolving correctly.
As far as I can tell this is only an issue in LXC VPS. We have CWP7 with Apache+NginX+Varnish Cache running fine in KVM and on dedicated servers. It's probably not an CWP7 bug, but a LXC bug. Anyway we'll just stick to KVM for now.
If anyone gets CWP7 running with Apache+NginX in an LXC VPS please update this thread so we know it works.