How to Estimate Power to Ground Current?
Recognizing that your driver will never have a zero ohm source impedance, there will be an expected upper limit that it can reach in a true short circuit condition. You should be able to estimate this value. Then by applying a low resistance current shunt in series with the "short", you can measure the near short circuit condition. For example, a shunt of 0.01 ohms would allow you to measure up to 1200 amps.

You will need to include all resistances associated with the short circuit apparatus in your final measurement results. This includes connector resistances, wire resistance, relay contact resistances, etc. In order to reduce the relay contact resistance, you may wish to consider an industrial control "contactor" which is essentially a heavy duty relay designed for high current applications.