Not really. There's only ~65% odds they Reset out of the IMM on the order you attempt to put them Unc. I'd hardly call 2 orders and ~15% odds (assuming ~40% odds of doing only a single wound) of success 'nigh-impossible'. OTOH it is clearly sub-optimal but that's evidently a feature, not a bug.
Simultaneity wouldn't really allow room for CoC to work the way you want either, you're still left with: "Model X was the LT when they entered a null state they never returned from" you just then also append "and CoC kicked in at the same time" Any interpretation where the model in question isn't the LT when doing the mission check is not simultaneous, it's applying CoC first. I agree that it's a bit frustrating that CoC is actually a liability in these missions, but the RAW doesn't leave much room there.
As written I agree, but we're dealing with a free form answer in an FAQ not a set of rules text, so asking for clarity regarding what timing they had in mind for the two effects is absolutely called for.
Unless CoC is involved, they'll still be the LT until the start of the player's next turn, so putting them Unconscious and then IMM should be fine.
This is what happens when you stare into the abyss too long. I literally had this right in my first post and then screwed it up. Oh well.
Special skills stop working when you're unconscious, and the LoL rules themselves imply that a lieutenant stops being a lieutenant when they enter a null state.
If, during the Tactical Phase of the Active Turn, the Active Player lacks a Lieutenant because they did not deploy or the previous Lieutenant is currently in a Null (Unconscious, Dead, Sepsitorized...)]] or Isolated state, then a situation of Loss of Lieutenant is automatically declared. Notice that at this point it's not a matter of "your Lieutenant is in a null state, and thus you must choose a new one" but rather you don't have one at that point, period. Like other skills, Lieutenant stops working once you go unconscious and you lose your Lieutenant as soon as the old one goes into a null state. Of course I can bet that CB didn't think that hard about it when they made their FAQ ruling.
You're misreading/misrepresenting the text you quoted. Logically, it's 'if you don't have a Lieutenant, OR your previous LT is in a Null state etc.'. Two separate clauses. The other issue is that the LT Skill includes: During the Tactical Phase, if your army's Lieutenant is in a Null state (Unconscious, Dead...) or is not yet deployed on the game table, apply the Loss of Lieutenant. My emphasis. Thirdly, LT is a status as much as a Skill, as the only trooper that ever has the Lieutenant Special Skill is the one that you initially choose in your army list.
Bummer. Awkward wording used there, maybe it makes more sense in Spanish. Lame that Chain of Command protects Lts in that mission from the "club 'em and stun 'em" trick. Tohaa are even more of a powerhouse in this mission.