I think you've nailed it; one thing, though:
Big Head Zach said:
Now, there's not really a surrepticious way of (using the Resurrection Ship to pass off a loyalty card) so the next thing that happens is that someone jumps on Admiral's Quarters (or Executive Orders the President, who has the equivalent Quorum card) and throws the new sleeper into the Brig. Sleeper then should just reveal the Cylon card and join the fleet (they lose the ability on their Cylon card for activating while inside the Brig, but there's not much else they can do). Now if the next person to take their turn is the newly-appointed sleeper....*wrings hands menacingly*.
It's true that there's no "subtle" way of passing off a loyalty card, but remember that your second loyalty card is most likely a "You are not a Cylon" card. The other player's will know that, so if you do pass a card off, they will no there's a strong possibility that you are just doing it to create confusion, suspicion, and dissent (incidentally, I recommend passing off "You are not a Cylon" cards to create confusion, suspcision, and dissent). So receiving a loyalty card from a revealed Cylon is not necessarily a one-way ticket to the brig; it just means that you'll be under a lot more suspicion. I've received a loyalty card from a revealed Cylon, and been able to convince the crew that I was a full-blooded human.
Also, I'd like to add this:
The Thematic Distinction of the Cylon Sympathizer.
The Cylon Sympathizer may be a Cylon that sympathizes with the humans, or a human that sympathizes with the Cylons, depending on what the resource dials are at.
If one of the resource dials is in the red, the Cylon Sympathizer is a Cylon that sympathizes with the humans. For the rest of the game, the Cylon Sympathizer character is a Cylon that has switched to the human side (since it's possible for the Cylon Sympathizer to have an additional "You Are A Cylon" card, it's possible this "sympathy" is actually a bluff). That's why this kind of Sympathizer is immediately thrown in the Brig. No one trusts a Cylon, even if they've decided to side with the humans.
If all of the resource dials are in the blue, the Cylon Symapthizer is a human that sympathizes with the Cylons. Along the lines of Adama's famous speech which starts the series, this is a human that doesn't think humanity has proved itself worthy of survival, and has joined the Cylon side. He or she is not a true Cylon (doesn't get a Super Crisis Card and can't control the fleet), but still sabotages humanity at every turn.
This doesn't change any of the mechanics you've confirmed above, it just allows you to understand what the mechanic thematically represents. Example:
If Saul Tigh gets the Sympathizer card during the sleeper phase, and one of the resource dials is in the red, it means that Saul Tigh was a sleeper agent, a Cylon, but has decided to remain loyal to the humans. For all game mechanical purposes, he is a human, and if the humans win, he wins. But thematically, he is a Cylon.
If Saul Tigh gets the Sympathizer card during the sleeper phase, and all of the resource dials are in the blue, the Saul Tigh is a human that has decided to turn against humanity. For all game mechanical purposes, he is a revealed Cylon for the remainder of the game. If the Cylons win, he wins. But thematically, he is a human.