Terminal: map super/command key in stty
@Niklas I solved the problem, but not using stty. Instead, I've been using Karabiner-Elements to do custom configuration on the Terminal keys (without affecting the rest of my bindings).

Basically you install the Karabiner-Elements app and then write a "complex modifications" rule in the karabiner.json file to swap whatever you want. Here is a guide on how to configure the json config.

My karabiner.json looks something like this:

{
  "name" : "com.apple.Terminal",
  "simple_modifications" : {
    "left_option" : "left_control",
    "left_command" : "left_option",
    "right_control" : "right_command",
    "right_option" : "right_control",
    "right_command" : "right_option",
    "left_control" : "left_command"
  },
  "complex_modifications" : {
    "rules" : [
      {
        "manipulators" : [
          {
            "to" : [
              {
                "key_code" : "c",
                "modifiers" : [
                  "left_command"
                ]
              }
            ],
            "type" : "basic",
            "from" : {
              "key_code" : "c",
              "modifiers" : {
                "mandatory" : [
                  "left_control"
                ],
                "optional" : [
                  "any"
                ]
              }
           }
        ]
      },
      ... more rules for all the stty characters, etc
    ]
  }
}