Osage is far from ideal for a hornbow core - regardless of design. It is oily, heavily ring porous and a bit too dense.
Compression abilities etc of a selfbow bowwood are irelavent in the core wood of a composite. It will make no difference to the performance. The wood is there simply to give the bow its shape and its stability.
If I were you I would definitely save the osage for where it shines and use maple or bamboo for the core.
How many historical hornbows had osage cores!? All these sort of questions have been answered/tried/ etc and the consensus remains. No need to re-invent the wheel
I have made osage cored hornbows before and you will have to use a modern epoxy for a good horn/core bond.