Then don't press it twice
Super+k is bound as the first part in several chains in the default Sublime keybindings. Look in
Packages/Default/Default (OSX).sublime-keymap to see what they are. For example,
super+k, super+k deletes to the end of line (as you've discovered).
Now, moving on to Origami's keybindings...
Super+k, super+right to create an empty pane on the right
Super+k, shift+right to move the current file to the pane on the right
Similarly, for the left. I hope this makes sense.
Incidentally, I find Origami's bindings to be too complex for my infrequent use of them. You may want to use the menu until stuff starts to make sense. I've also put together a set of commands (four posts up) that can be accessed from the palette. To use these, copy & paste them in a file called, say,
Origami.sublime-commands and put in your Packages/User directory. This is much slower than using the keybindings, but more reliable (for my weary brain, at least).