I'm completely new to Inquisimunda, but I've played a lot of Necromunda (the LRB edition, not the community edition).
I like that your current draft fixes my main gripe with 2.0: no good way to make an Adepta Sororitas warband (either have to be Inquisitorial and not have enclosed PA - as if the girls all lost their helmets, or be Ecclesiarchical and not have PA+special/heavy). However, I am concerned about balance with them as part of the 'cult' warband - Sisters are a proper military force and should have access to a lot of ancillary gear/equipment - so either stuff that shouldn't be available to cults will wind up available to cults, the list of 'extra gear' under Ecclessiarchy will get really big, or Sisters won't have things they should have.
Perhaps it would be better to divorce Sisters from the Cult list and put them as a Military or Inquisition list variant instead. Generally, the Sisters wouldn't operate as part of an individual cult and instead would be their own convent answerable to their Prioress or Canoness. I think that Militant cults that violate the Decree Passive would be highly unlikely to have a legitimate Battle Sister present - the stated purpose of the Sisters of Battle is to not only prosecute wars of faith and defend shrine-holdings, but also to watch the Ecclesiarchy itself for heresy or abuses of power - so a cult like the Red Redemption or in general any militarized cult would probably be in hot water with the Sisterhood.
Tangent: The only reason the Adepta Sororitas still exist after the Reign of Blood and the Terran Crusade is because Alicia Dominica - after being taken by the Custodes to the Throneroom to receive some secret knowledge - executed the mad Ecclesiarch. Individual sisters might be loaned to high-ranking Ecclesiarchy officials (as often as watchdogs as honorguard), but in general they are a parallel organization to the clergy rather than an integrated one - and even though it hasn't happened since the Terran Crusade, the Sisterhood still exists as much as a check against corruption in the clergy as anything else (hence why they make a natural ally to Puritan Ordo Hereticus Inquisitors - albiet with some friction since the two organisations serve similar purposes).
/Tangent
Add to this the fact that the Sisters of Battle are only a single arm of the Adepta Sororitas (the other arms being Dialogus, Hospitaller, Famulous, etc), and in my personal opinion the best place for them is the Inquisitorial warband entry as a variant (Palatine instead of Interogator, Dialogus instead of Sage, etc etc) with a couple of extra gear options and restrictions (the biggest restriction: every member other than a Dialogus or Hospitaller MUST purchase power-armor... as per the novels, even Sisters novitiates are in power armor if they see combat - making a pure Sisters warband necessarily small).
Thought/Idea: Doing this would mean that while an Inquisitor might have a few battle sisters (acolytes with power-armor, mechanically), only a pure Sisters force led by a Palatine would have access to the more exotic options such as jump packs.
Tangentially related Addendum: Sisters of Silence are focused on investigation and apprehending rogue psykers - they are to-a-woman abhuman Blanks, but would be considered a Puritan organization by even the most hard-lined Inquisitor. Perhaps a note in the Inquisition section that allows a Puritan Inquisition warband to take abhuman blanks as members so long as those blanks purchase Power Armor in order to represent Sisters of Silence?