Very well played. You should stream sometime.
The Doom is mostly there as a big "if you forget me, I'll kill your Eschaton" factor, but if you have to, you can just deflect its torpedoes away, which means you do have an ability to pressure it. You just can't easily destroy it.
Logistics stats will put it on the level of a battlecruiser, roughly, with additional strain in the form of very harsh hyperspace fuel consumption and repair rate. I feel like this is a fair tradeoff for the potential damage you can deal in that ship, and how it can turn the crossfire of an entire fleet battle against the enemy...
in theoryIt'll also cost a ton, almost twice as much as a Nevermore.