You could make 120 degree angled braces that tab into the top edge of the hex fence, (and maybe the middle too) they’d probably give it some good rigidity.
Take a look at @geek2nurse’s latest icosahedron for a good example.
You might need to use plywood on the connectors to make it strong enough… hardwoods will want to split along the grain. Not saying it can’t be done, but it will add a level of difficulty.
You could also make your hex sides finger joint into each other. That’d add a lot of stability.