I was able to resolve this, but I am not sure exactly why. To simplify my post, I removed the code that sets a variable for the base path. That's where the problem is.

set $homedir /webspace/mydomain.com;
root ${homedir}/www;
access_log ${homedir}/log/access.log;

The root works, but access_log did not. NGINX would prepend /usr/share/nginx/ to it every time and result in the error from my original post.

If I don't use the variable, it works fine.

access_log /webspace/mydomain.com/log/access.log;

It kind of defeats the purpose of having a variable, but at least it is working now.