Sounds very samura industries to me.
The thing is, most corporation in Sirius could build battleship, and man them. The problem is, how could they deploy such things efficiently in a strategic way? beside, do they really need any with all the influence they have on the houses?
let's move on shipbuilding corporation though. They actually could begin selling battleships, but who would buy them? We have already removed corporation. Houses navy or police wont use them as they have their line.
That leaves the criminals and the neutrals.
We must remove every criminal and neutrals that have their own line of ships, or are known to use their allie's line of ships.
We might have junkers. While being someone who is opposed to junkers ever getting their line of capital warship, rich junkers could decide to have their own little mobile palace: a mobile smuggling vessel, less powerful than standard naval battleship, yet capable of defending itself.
But you'll see another reason, they will follow in my following explanations.
We might have Xenos. In their desperate cause, they probably have gained a few more people in the last few years with the social unstability, mostly coming from outside liberty. I can predict some strong sense of isolationism already spreading. Xenos are probably in this moment, gaining recognition in the liberty young, rebelious people. With secret supports, they might be able to aquire a few of these warships - probably through dealing with the junkers of course. They will of course be a very rare sight, Xenos being very restricted economically.
The unioners. Not only were they the workers of the Rheinland shipyards, they knew how to maintain a ship, because they built them, and maintained them til a customer such as the RM buy the ship.
Unioners should hence be able to live with a few battleships here and there as their mobile headquarters. I imagine they might have stolen a few older model when they formented rebellion. And through again the very long arms of the Junker, (which I always seen as an extremely powerful underground market), they might manage to possess a few more.