Old school liquid thermometers demonstrate this beautifully.

We’re talking about clay pots here. How would you get the crown into the narrow opening? If you have two containers, one for displacement, the other for measurement, you would lose far more water in the pouring than the precision required.

Here is an idea: I can imagine a vessel that looks like an elongated tetrahedron upside-down with one of the isosceles faces open and the point below it beveled to enable it to balance in two positions, position 1 with the long end slightly higher than the short end, and position 2 with the long end exactly the same height as the short end. Start in position 1, fill with water, place the crown to overflow it’s volume, then remove the crown, tip the vessel to position 2, mark the extent (rather than the height) of the water on the elongated end, repeat with the gold, compare.

This could be improvised with something like a large urn and a block to lift the long end a little bit. I’m still not sure about the precision of the overflow and dripping off the water.