Thankfully with this setup, you can do most everything with the GenerateBlocks interface.

The container, container background, darker border, and shadow are all done inside of GenerateBlocks, with only the thick white outline done with CSS.
.double-border {
outline: 10px solid white;
}
You can swap out the outline color in the CSS for whatever color your background is for a nice subtle effect (like you see in this example on white with a white outline).