Wow, in 7 years of daily Linux use, I somehow never thought of doing this. Thank you.

~/.bashrc:

stty intr ^x

~/.inputrc (at the end):

"\C-v": "" # Unbind Ctrl-V

~/.config/terminator/config (in case anyone happens to be using terminator):

[keybindings]

  copy = <Control>C

  paste = <Control>V