Deer antler? It should have the required strength and about the right density; but it might not be so easy to find one with a straight section 12’’ long.
I believe they could include mineral as natural material seems to be the guideline. The amount of processing used might be up for debate if it were a close call.
Antler might be tricky (although it is an excellent material - heavy and tough).
How about a sliver of horn from a gazelle? Gemsbok have very straight, long horns - and they are not brittle (people make bow arms out of them).
How about natural bamboo, drilled hollow and packed with a mix of resin (or animal glue) and powdered iron ore?. Once it’s set up, the knuckles and other surface imperfections of the bamboo could be smoothed away.
Antelope horn - specifically, gemsbok horn- can be found in the lengths you need & is machinable (it’s used for custom knife handles) but I have no idea of the density other than it’s like a hard plastic and IME denser and stronger than bovine horn, if you’ve ever used that for nocks or tips.
ETA - I see I’m ninja’d by Mangetout - but I brought a link!
We use a lot of mosso bamboo presently, very heavy stuff and currently our best material. Hard to work with in very small diameters.
I have some of this home, I use it in some bows i make, not stiff enough in the small diameters also issues with straightness.
I think we might be back to a section of animal bone then - If you can get hold of one of the longer bones from the leg of a cow, horse or maybe deer, I think there could be some way to get a 12"+ straight solid piece out of it (although ironically, the quickest way to know this for sure would be very unprimitive - a 3D medical scan of the bone would reveal whether there is away to cut a piece of the right length and straightness out of it)
I’m nearly certain a giraffe leg bone would have enough of the right material (and surely has to be strong/dense enough), but could be difficult to source.
Not if you have contacts at a Danish zoo.
StG
You could try making paper or even fabric, then rolling and lacquering it into a tight cone with a bit of stone in the tip for weight.