As for assassinating Mitsuhide, I don't think that's an option here. If it was, then I have to imagine Inquisitor Harker would have had us do so the second he discovered she was messing around with a can of worms that the Emperor personally ordered sealed for all eternity. My money's on the Inquisition by and large disapproving of extrajudicial killings of their members. The Radicals because they want the protection a Tribunal provides, the Puritans because killing prominent Imperial power players without hard proof is one way Puritans slowly become Radicals.
I don't think assassinating her is as off the table as you say it is.
But even if you're right, then we do have another option the Inquisition will be much more willing to accept; Kidnapping and Containment on suspicion of Genestealer infection. After all, nobody can assume innocence where filthy mind-stealing xenos is involved.
We'll have to wait for the next turn to tell us exactly what Severus knows so we can spin it properly, but there's a huge difference between, say, marching a few thousand Guardsman off to die in stupid fashion, and crippling Sector-wide logistics by murdering (or allowing the murder) of a high Administratum official. One would demand they replace a WHOOOOOOOLE lot of people, the other is a much more serious crime with a smaller group of criminals to punish and gives a lot more social/political wiggle room for us to make a mess.
As for voting, I'm struggling to come up with a write-in that maximizes our chances, so here's a stopgap vote;
-[] Punch through the Encirclement: While the Cult of the Four-Armed Emperor still surrounds the palace, a concentrated push by the remaining forces might penetrate their lines and allow you to reagroup with the rest of Imperial forces, taking the Lord Sector with you.
Whatever we do, we cannot stay here because the two biggest and most competent field commanders - us and the General - cannot afford to remain stuck under enemy encirclement while assholes and traitors run around in the background.
Given that we won by narrowest margins last time and this is very shortly afterwards, I see this as our high-certainty high-risk move; we'll probably break out with our VIPs intact, but it's probably going to hurt.
-[] Sneaking through the Underground: Taking a page from the cult's own attempt, you might try to sneak the Lord Sector alongside a Mist Shrike escort through the sewers.
This one plays to our current strengths - small elite units - and minimizes damage, but increases the likelihood that said damage will be VIPs.
@ThunderOwl I'd like your feedback on a question;
-[] Extraction by Air
How likely is it that the Cultists have sub-orbital capable AA, and in Severus' opinion would doing a vertical burn to sub-orbit, then sub-orbit hopping to the nearest Astartes-populated friendly airspace maximize the overall (of all possible options) chances of getting the VIPs away safely?
Because if there's one thing that Thunderhawks excel at that most other Imperial-available craft don't, it's the ability to go cleanly from space to ground and vice versa at high speeds.