Im not the TT guru, but here goes:
The easiest way to get the lowest Ra (resistance of the electrode, and cable to it) is to go deep,. The deeper the better. This is because as you go deeper, the moisture content in the soil increases, and becomes less dependant on the weather conditions. Also the ground wont freeze.
If you hit rock, the the other option is to use another electrode position. This must be sited at least the distance equal to the depth of the longest of the electrode away. So say you have an electrode of 6m depth. The nearest you could place another electrode is 6m away.
You could lay tapes or mats ect to try and lower your reading, but youd have to dig a deep hole, and you probably wouldnt get a much better result than a deep rod. Rod thickness doesnt have a great influence on the resistance, neitrher does the copper content. Rust doesnt have much of an effect either, as it will conduct better than the soil around it. As long as the connection from the cabl;e to the rod is non corroding, then thats ok. We use Denzo tape/paste at work.
The last resort is soil conditioners, but they will undoubtably be expesnive (ive never used them), and i reckon thatb you would have to reapply at set intervals to maintain a low Ra.