I know this will speed up the site, but this is not a solution for this issue. The problem is that the magento 1.9 standard is not used, so it has to rebuild the menu all the time. Your theme says that it support magento 1.9, so this should work like the magento 1.9 standard. It has nothing to do with varnish cache or other caching methods.

We shoudn’t have to install extensional caching methods to get a ‘normal’ speed on a theme.