The test described previously is the "water replacement test". It is an ASTM test I believe. When I did that testing for a dam job, we had a heavy steel ring fabricated about 6 feet in diameter placed onto the test area. Our rock was significantly larger, so the size of the ring for the material that you have described can be significantly smaller. We dug the gravel out from inside the ring with a mini-excavator. Hopefully you have a means to weigh a large mass like that. Anyway, fill a large, sturdy container with the material that comes out of the hole and weigh it (after obtaining a tare weight of course). Then the volume of the hole is determined by laying out the poly sheet and securing it with the ring. Fill it with water to get the volume.
To determine the maximum density, you need to use something like that same container, but this time compact the material in lifts into the container using a plate tamper and determine the maximum weight after a few trials. You have to be careful to ensure that the voids at the top of the last lift are roughly the same by volume as the protrusions sticking out of the top of the container.
Also, I think it is vitally important to have me come over and conduct the test utilizing my vast array of experience with it...you did say it was a coral island in the Pacific right?