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You shouldn’t be installing as root anyway. Use a virtualenv in your allocated directory, and install everything in there. You should be using a virtualenv in development as well, so that you can create a requirements file as part of your codebase which can then be used to rebuild everything in production.
If the host doesn’t include mod_wsgi, there are plenty of alternatives these days. Mostly I’m using gunicorn for my projects; it’s easy to set up and you can run it yourself, with Apache or nginx simply working as a reverse proxy to send requests there.
However, that does depend on the ability to run long-running processes on your host; if they don’t allow that (some don’t), it’s a problem. An alternative might be FCGI though, although at this point I’d probably be looking for an alternative host.