Yes, it is the design of the piece that makes it awkward to wear, in my view. I should have made that clearer.
The necklace itself is OK but not for that gem. The two do not go well together.

Perhaps the opal would be more wearable as a brooch.
I picture it horizontal but angled somewhat , and appearing to float inside a largish asymmetrical (rectangular) surround composed of a number of asymmetrical pieces of something. Gold? Silver? Enamels?
And such a brooch could be worn pendant from a very fine silver or gold chain only - attached to the top corners.

That's more than enough of my ideas.