One thought, I believe there is a module that will backup the full DNN database and File system, now where it will save those files I am not sure, but I think you can use it to make local copies of your whole site.

I just checked, there are a few available, so you might need to research a few of them. They are a bit pricy but not too too bad. I would email / contact each of them explain your situation and what you would like to do, and see if they state their software will do so. Of course this is making the assumption your host has not blocked your ability to install modules.