This should be a concern whether it is perfectly flat or not. You should be talking to him ahead of time about how to attach it safely, otherwise the customer might think you made them a faulty counter when it cracks.
Play with the spacing and the arch just a bit, and you have room for another set of drawers. Unless you plan to execute some killer joinery to show off, I'd probably go with side panels to emulate the drawer fronts.
I agree that the arch looks too thick in the front. I usually define arches by the difference between the height at the center and the height at the edge. For that size the difference should be around an inch. Try two inches thick in the center and three inches thick on the edge and see how that looks
You can add a skirt under the top to make the piece more balanced.
For the sides, I think a solid panel would be fine but a bit boring. Some ideas are a solid panel over the bottom and arts and crafts slats on the top, headboard, or arts and crafts slats top to bottom to expose the drawer.