Video version of this guide now available: https://www.youtube.com/watch?v=oRnpbsm56TE

Hi. I've spent the entire day getting all the endings of Sunrider's new alternative-universe expansion. Here's some tips on preventing the Liberation Day Massacre.

The decisions that you make during the first battle (to save or not to save the crew member) and when you're deciding on how to abduct Chigara (with or without Lynn as a double) determine how early you'll get noticed. Wrong decisions during the battle also lead to two bad ends as you're killed by the attack drone (Bad End: Gunned Down / Crushed).
If you've blown your cover saving the crewmember and didn't use Lynn, then the present!Kayto will be clued in immediately, and marines will bust your door down just as Chigara is waking up. Somewhat counter-intuitively, this rash approach is the only way to get the good endings: this way, you'll get captured before you're able to tell Chigara that she's a Cylon prototype, which would have lead to her immediately getting controlled and shutting the ship down.
If you haven't blown your cover at all, and the route isn't Ava's, you will escape immediate capture after Chigara shuts everything down. You can reach all the neutral ends this way.
If you've gotten noticed at first, but then decided to try going stealthily (or vice versa), you'll get busted right after Chigara shuts everything down, and you'll have to escape the brig first to get your message to Fontana. This will take too long, and you'll have a bad time in hard vacuum as the Sunrider gets blown up by Alice (Bad End: Explosive Decompression). This doesn't happen on Ava's route, as she lets you out soon enough to not die.

In any route, you're prompted to decide on stealing Claude's holo. It's important for getting Ava on your side in order to escape the brig after you're captured. This is obviously not important on Ava's route; additionally, it's not important on Icari's (as she can break you out herself). On Asaga's and Sola's routes, though, you can get stuck in the brig as Ava won't let you out without the evidence... and then you'll stay there until the massacre, and then you'll die when present!Kayto rams the Machiavelli. And the chosen girl will die with you, having been shot during the massacre (Bad End: Trapped - Sola/Asaga versions).
The same thing happens on Ava's route if you try to run away from the marines as they're capturing you. You get shot so full of stun blasts that you go comatose until the massacre (Bad End: Trapped - Ava).

That decision is actually not important most of the time, save for an Icari route where you let the ship get shut down. This is the only time when you go into the frozen service tunnels to send the message to Fontana alone, so there's nobody to keep warm with. And, well, you'll die (Bad End - Frozen) if you've told Claude off. If you haven't, she comes to your aid with the power of warm chest rockets.

If the Sunrider is shut down, but you haven't wasted too much time (or you're on Ava's route), you'll be able to fix the reactor. Right after that, you'll be confronted by the present!Kayto and the marines. This leads to "neutral" endings, as follows:
-Ava: "Maiden's Suicide". You surrender. Future!Claude replaces the present!Claude and doesn't stop Asaga as she has her breakdown and flies to kill Chigara. They both die, but the massacre is averted.
-Icari: surprise, it's actually Claude's ending. It's funny (Claude's Secret Ending).
-Asaga and Sola: you fight your way out and escape on the Blackjack / Seraphim. For Sola, there's one other variant, but it's... well, it's not called "the worst end" for nothing, go there at own risk (Sola: What Have I Done).
If you've escaped, you skip on all the action and camp out the Liberation Day ceremony, with intent to shoot Chigara before she gets controlled by Alice and kills everyone. If you go through with this, there's a rather depressing ending (Asaga/Sola: Future Won With Blood). If you don't, you're dropped back into Liberation Day canon, although you now have a connection with the pilot (Asaga/Sola: Still Together).

Again, these happen only if you took the rash approach (saved the crewmember, then didn't use Lynn) and Chigara didn't shut down the ship, and you also have a way out of confinement (on Ava's and Icari's routes you have one by default, on the others you have to steal the holo; also, on Ava's route it doesn't matter if you've blown your cover or not as she's the one who notices you on the other routes).
After escaping, if on Ava's or Sola's route, you'll be presented with the decision of either having Chigara killed by Asaga (leads to Ava's neutral ending and Sola's worst ending), or convincing the present!Kayto to help you. If you've decided to convince (or you're on Asaga's or Icari's route and haven't had to make this decision), that's a Good End. You save everyone, and you get the hawt seks. Hooray!