What would be our Logistics priorities, actually?
This is just my opinion, and could be completely thrown off by what we get on Turn 6, with Chuck out of the way. I am operating under the assumption that we get some Badnik factories and metal mines, which is not a guarantee, but not all of it..
1, Egg Drones or Ring Reactor
2, Honey's Shop.
Ring Reactor lowers a bunch of DCs and lets us start making Tier 3 Badniks if we want. It serves a lot of big needs, but might not help as much with the current situation.
The Egg Drones are lower DC, meaning we can throw Starline at it with more confidence to prevent him from getting a drive malus, help prevent further infiltration when Whisper and it'll help us look for items in the future. Such as the conch, if it turns out we really need it.
Honey's shop gets us income and her loyalty up. The sooner on the former, the better for the sake of building up towards Elizabeth. Especially once we go to the Black Market, since the more money we have the better options we might have as well.
If we do not have enough Badnik factories, then we need to build one. They are meant to be our disposable troops, but we've been hemorrhaging them faster than we can replenish. We also want troops left over for after we beat Zavok, so we can actually hold on to territory once people are more likely to go for us. Especially since we've just pissed off a King in Gouji, if he can trace it to us.
Might also be worth starting the X Super Badnik gacha, since it auto-generates a Tier 3 Badnik for us every turn if we can afford it, but we don't know what the cost or DC will be yet. Might be a next turn kind of thing, along with a Ragnite mine.
We just need to unlock the bluprints for them into the PA also according to the QMs we could have unlock better ones than the Death Egg Robot and would be able to build them before the Raid, so I guess it depends what kind of mech you can unlock there.
I would like to point out that it's a multi-turn process.
Turn 1, take PA.
Turn 2, build mech (if possible)
Turn 3, Get to use mech offensively.
We got to use it in the raid because Zavok came to us. If we went to him, probably would not be an option.
Building mechs very much seems like something you typically do in advance. Not while you're trying to finish somebody off unless you're doing so well on that that you can afford to dedicate actions to something else.
I think it needs to be done, just... highly unlikely that it will be before beating Zavok.