How do I ground this system?
Don't. You can't, anyway. Whatever connection you make will be long enough that it will be more of an antenna than a ground. But don't worry, you don't really need a ground anyway.
Why would you need a ground? One reason is lightning protection, but that's probably not what you hand in mind, and it's more complicated than running some wires to some dirt. You should read more about it in a separate question.
The other reason is to give common-mode currents some place to go. Due to the law of charge conservation, any common-mode current must be accompanied an opposite current somewhere else in the universe, and usually that thing is the Earth. By grounding the feedline somewhere, you short out these currents.
But it's really better if you just have no common-mode currents in the first place. Anywhere there's common-mode current on your feedline, it's radiating. And by reciprocity, that means it's also receiving. In effect, it's part of the antenna, and usually that's not what you expect.
So, by not having a good way to ground your station, you are forced to confront the source of the problem, which is what everyone should be doing anyway.
Put baluns on your antennas if they need them. With a properly current-balanced antenna, you won't have any significant common-mode currents due to your transmissions, so you won't have any problems with RF in the shack.
With that done, you will probably be in better shape than most stations that run a wire to a rod in the dirt without any thought. For further reading, I suggest W8JI's article on station grounding.