quite soluble. That's the reason why NaCl in Microdol-X increases its solvent property, and why a saturated NaCl solution can even work as make shift fixer for Silver Chloride paper. You read correctly, NaCl won't fix AgBr or AgI, because AgBr is by orders of magnitude less soluble, so you can't fix film that way, at least not to archival standards.
Conclusion: CuCl2 might work well if diluted, but once you make it more concentrated, it will eat away some of the Silver Chloride just formed. By adding KBr you form mostly AgBr, not AgCl, and that won't be dissolved in quantity by Chloride.