A fan has translated a PSP Evangelion dating sim/visual novel side story that explores Shinji’s relationships with Asuka and Rei in a more peaceful alternate reality.
Shinseiki Evangelion: Koutetsu no Girlfriend 2nd -portable-, or Neon Genesis Evangelion: Girlfriend of Steel 2nd, has players exploring an alternate universe where they can date Rei, Asuka, and Kaworu, unlocking various CG scenes for getting to know them better. The alternate universe here is one witnessed during an episode of the series where Tokyo-3 was at peace.
The English patch for the game is available through the translator’s site, although the translator says there may be remaining bugs in some of the player routes. An English patch for the PC version of the game came out some time ago.