Which type of lay-flat binding to use – choosing a printer

I’m about to reprint my two specialty cookbooks and want to use a new version of lay-flat binding. I’ve used a semi-concealed (wrap-around cover) binding, where the wires and holes are visible on the back. It’s nice but the front cover is “sloppy” and moves around, plus the cover gets crushed into the wires when the printer shrink-wraps the stacks of five. I’ve gotten bids (hard to find in the US) for a binding called “double- wire-o split binding” where the spine shows through in between two separate sections of wire-o at the top and bottom. Has anyone used this? How does the durability compare to a full-length wire-o? What is the minimum pt cover weight I should use? I’ve been using 12 pt C1S, but wondered if I’d have to bump it up in stiffness. All comments/input appreciated.