OK, so, medieval crossbows were all about raw power and never mind the efficiency, they used a brick-wall type structure of very narrow horn slats laid flat and built up as a wall thereby avoiding the horn delaminating - a 10mm thick strip of horn will de-laminate very quickly if you try and bend it very far. A 10mm thick horn structure with a 10mm thick layer of sinew is good for 250lb but cutting all those horn strips, straightening them, grooving them, gluing them together and then shredding all that sinew and laying it on and then leaving it for 12 to 24 months to cure is a lot of work. Trust me I know.