Thanks for passing that along. First off, caching, plugins, and Jetpack are not theme-related issues. :-)
You have a ton of database errors in your logs:
WordPress database error Lost connection to MySQL server
WordPress database error MySQL server has gone away
Database connection errors could certainly cause the issues you describe with your site timing out.
They are not caused by a particular theme.
You may want to think about reinstalling WordPress from a fresh copy after ruling out other issues. To rule out other issues:
- try a default theme temporarily
- try turning off all plugins temporarily
- try a traceroute as I mentioned above.
I also suggest you remove that error log from the public folder as it could be a security risk to expose it publicly like that.