You should not be setting connect-timeout so high. The default is 15 seconds. That timeout only covers being able to create the TCP socket connection to the listener socket of the daemon process. Nothing to do with how long requests take to be handled.
Anyway, what is the remainder of your configuration for mod_wsgi? What is WSGIApplicationGroup and WSGIScriptAlias set to?
What are all the log messages being put out by mod_wsgi at the time this occurs. Ensure you are using Apache LogLevel of info rather than err or warn. Using info will result in more about what mod_wsgi is doing being displayed.
If I had to guess, it would be that you are not setting:
WSGIApplicationGroup %{GLOBAL}
resulting in your application running in a Python sub interpreter, but you are using a Python package which uses a C extension where the C extension doesn't work properly in a sub interpreter. This can result in a thread deadlock and the sort of problem you are seeing.
So if only have the one WSGI application, set that WSGIApplicationGroup directive.
BTW, if you do need a timeout on requests, use request-timeout with WSGIDaemonProcess.
Finally, you should not need to add /usr/lib64/python3.4/site-packages to python-path. If that is required, there is something broken about your setup, perhaps including that mod_wsgi is not compiled for that Python version.