Oh wow, great idea! Now that I'm working more often with linux, I kinda got Caps+C etc. in my muscle memory, because I set Caps as Ctrl. When I switch back to macOS, it takes a while of wondering why my shortcuts won't work.
Care to explain how exactly you set this up? I guess in System Preferences -> Keyboard you set Caps to Cmd. And then?
In iTerm Preferences, Keys, set Left Command to Control, then in the Key Mappings list, add each Cmd-xyz combo you want to preserve, and set its action to "Do Not Remap Modifiers".