The 710 μF is relative to infinite distance. That's what you would see with a setup a million kilometers away and a cable going to Earth. If you have a setup in your lab then you never change the overall charge of Earth because that sum includes your lab. You can exchange charge with Earth with the only limit coming from your lab setup. It's a bit like to charging a capacitor in a circuit: You don't calculate the capacitance of the overall capacitor to infinity because all the charge re-distribution is internal to the capacitor.