From a dev perspective, the 'intended' method of approaching this - though obviously it's fine to go about it in many ways that's what the open-world game is for! - is to, after having once won the Election and then received the big reveal, to return to the beginning and hunt for evidence to prove that fbzrbar vf ylvat nobhg jung unccrarq gb lbhe sngure . Because normally if you try to investigate that, all three of your options of what to say about it are clearly wrong, which you the player know because you've seen the main ending.
There are MANY pieces of evidence scattered around the game that you can use to give you an idea that something funky is going on and thus unlock the extra dialog option which sets you on a new plot direction, as long as you uncover at least one of those clues before you do the investigation. If you follow only that thread, you will arrive at an exciting event with a whole bunch of Bad Ends in front of you, which will then provide clues about what other information you need in order to get past it. (And once achievements and ending-graphic-collection are working, you'll have to do that at some point in order to see some of the variants.)