Hornbeam checks rather badly in my experience. Debark, reduce to rough dimensions, seal on all sides with wood glue (water soluble so you can wash it off afterwards) clamp the limbs to a board so it wont warp, store dry and wait a few weeks.
Trapping can be done on back or belly, generally done on the back hence the confusion.
Such rounded bows are sweet shooters but tend to be a bit slower as they are heavy (mass) for their draw weight: all the mass is concentrated in the neutral plane.
Try multiple ones. I would decrown one on the back and back it with wathever you can: sinew, sisal, bamboo, hickory, maple, ...
Joachim