I have always wondered if you couldn’t relatively easily use some other physical property to non destructively distinguish gold and tungsten. The speed of sound in gold is about 3240 m/s, in tungsten 5200. It should be relatively easy to instrument a test that measures the “ringing” of a bar in response to an acoustic signal, and use it to characterize gold vs. tungsten.
Mass=Volume/Density?
Ultrasound Testing of Gold Bars - Checking for Tungsten or other materials