Well, you've got Zao, the majority of the Imperial Naval (though not the Peleps and V'Neef Navies), and probably House Sesus. With Sesus comes Cynis. Nellens might be convinced to back the winner, and maybe your "Tepet lover" can deliver her house...
Your enemies, of course, will include House Cathak, the most militarily potent single organization in the Realm. And probably the Immaculate Order, since Syn controls that even more absolutely than Zao does the Admiralty.
And as I've mentioned before, the Imperial Navy is the Shield of the Realm. It is the piece that will take the brunt of any attacks on the Isle or any sabotage attempts, because Ahaha like the Lunars, Infernals, Dealthlords, wouldn't take this chance to gut it before this conflict is over. Which reduces how much we can use this in the civil war and forces us into new fronts of war against those threats while we are fighting whoever our opposition is.
With our previous Social Interactions, House Sesus is not trustworthy. While I do not doubt they will back us in battle, behind the scenes the chances of them prepping to back stab us or fuck with us once the war is finished is really high. And while Nilul could help us deal with them, that puts her at risk and divides our attention, which we can't really afford yet. Ideally, we do a lot of shit to solidify a bond with them before any civil war starts.
Nellens is immensely useful as a support, but like Sesus they are not exactly allies that we have a strong bond with yet. Nilul and Saery together could possibly hold them, but again it doesn't feel solid enough.
And Tepet, well look pretty sure that would attract the ED and her Redness like flies to honey. Also having Nilul do the social fu work on 3 Houses is asking too much of her.
And I know Pearl can help her in those things, but one Social is not really her focus and two she'll be busy countering the other Sidereals which reduces what she can do in the House Politics. It might still be enough, but it is cutting it a little close.
Basically, this is all the kind of stuff that would be a lot safer to do before a Civil war.