To expand on this:
Don't go back to that second mechanic. That is absolutely not going to be an issue on a z1000 of any year. Hearing a mechanic say something like that, brings into question their experience.
Measure the diameter of the handlebars and make sure those aren't aftermarket as well, if the previous owner was dumb enough to replace a dual throttle cable assembly with a cheap chinesium single pull, makes me wonder what other shit they cheaped out on.
That bottom set screw on the throttle assembly is waaaaaaay out, so that definitely doesn't fit.
Also check that the throttle body isn't gummed up with a bunch of lube, spray it down with brake cleaner if is, re lube with a couple drops at each pivot of triflow or similar lubricant. Too much lube will attract dirt and gum up the throttle, and a sticky throttle on a crotch rocket, with only a single pull cable, is a great way to become a meat crayon.
Lastly,
https://www.revzilla.com/oem/kawasaki/2013-kawasaki-z1000/throttle
I'm pretty sure the above blow apart diag should help you visualize what others in this thread are talking about and show you what parts you'll need.