[X] Siege. Reduce Linxia's orbital defences, this will leave the colonies around the gas giant completely at your mercy and allow you to loot them, you can bring in the captured cruisers once the defences are offline, sending the Cirrus back to guard them until that moment. (Reduction of planetary defences will take 1-3 days depending upon rolls. You do not know how much wealth might be on offer, but dozens of points worth).
Yep. We don't want to take on heavy orbital defenses at this point. Let's list off possible threats to our siege.
-Corvettes: According to our intel, only one corvette is in system, and said ship will have to be pulled out of reserves and brought here, likely taking days. A single corvette isn't much of a threat anyway, especially since it probably isn't at full readiness.
-Skiffs: Three skiffs are left in the system fleet. Attack skiffs are scary firepower-wise, sure, but our CL can pretty much one-shot them with decent rolls. Three sub-scale ships aren't going to be much of a threat, except they can screen for the monitor...
-Which brings us to the Monitor: The Monitor has us beat on combat stats, and it's a capital ship. It's clear from our intel that it lacks experienced crew, and the commanding officers probably aren't much better. Strauss's tactics are high enough that (although capital-scale hits hurt) we probably won't get at all. Once our CL finishes up with the skiffs, we'll be able to wear it down.
I'm thinking the most likely scenario if the system fleet commits to battle is a monitor and 3 skiffs. The multi-attack bonus is painful, but crew and XO bonuses for the CL will more or less bridge that gap. Cruiser hits will knock skiffs out of the fight entirely, while the skiffs won't be able to do meaningful damage. Meanwhile, Strauss + his ridiculous crew bonus should be able to easily hold off the monitor until the cruiser finishes up with the skiffs, and then chip away.