First of all, make sure your contractor strictly follows JH's best practices guide for your climate zone. As for the horizontal runs, they can't be avoided with JH siding. The z-flashing tends to disappear to most peoples' eyes. A one story house can likely avoid it. The other suggestion is a horizontal trim over it, but I don't prefer that solution. When I chose this system for this house, I didn't find it as a "full system" offered by JH. They suggested it and showed me their guidelines, but I don't know if one will find it as a complete solution as one would find lap siding, vertical siding or shakes. All the best on getting there.
Q