Great job Sleeper and KJ4VOV!!!
I just have a few comments and suggestions....
-"The boss gained some internal drones in phase two."
I'm not sure yet what exactly you changed here, but if the boss uses more than 4 drones it will not work because it's hard coded to never use more than 4 drones.

However, if you took out the (GODDDAMN!!!) Boarding Drone and replaced it with an Anti-Personnel or System Repair Drone that will work. Also think it is possible to get it tonuse more than 4 drones, but never at the same time, meaning if it lost a single power bar and it took 2 power for it to use a drone it might turn on a 1 power drone. (This might actually be a way to diversify the drones, but I haven't tested this out myself yet).
-"The Boss now uses a Heavy Defense Drone..."
I think because the CE drones are so much cooler you should change the Offensive Drones for the Boss as well. Personally I changed the flagship drones to a Heavy Laser Drone (2 power), Light Laser Drone (2 power), and Light Defense Mk(2?) (2 power .6 Cooldown). I do like that the Heavy Defense can shoot down lasers too though. I don't think either of the 2 offensive drones need to be there because the power surge calls a whole bunch of laser and beam drones, therefore the "main" 2 drones don't have to be laser and beam drones they could be more specialized offensive drones.
-Boss AI Takeover Event
I like this idea, but in order to make the boss more random could it be added as a random possibility? Like the possibility of having to fight in a sun, nebula, or asteroid? I think that would be a better choice.
Also, if you move the position of the drone room it will also be possible for the flagship to gain internal drones when the AI event is triggered. You could set the drone control power to be loss="4-8" at the beginning of every other event so it can't use drones and clear it or just not use loss="" for the AI event.
-Boss AI Takeover event acts as deadline for boarders
Does this mean you found some way to make them board when the AI takes over or not board until the ship is out of oxygen? If so awesome!!! You could also say instead of HAL9000 taking over that the crew is "abandoning ship," but they are leaving the remains in the hands of an advanced AI.
-"Placing Minefields costs one less missile"
I was actually wondering if you could make placing a minefield cost something like 6-10 or even more missiles, because it is a minefield after all. The trade off could be that the fleet is delayed by 2-3 turns though. I'm not sure exactly how broken this would be, but I think the trade off should be that you basically have to buy all the ammo at every store you visit to compensate for the huge missile requirement and the sectors you go to in the 2-3 extra jumps you have would need to give you just enough or slightly more scrap than it cost to buy the missiles.
That's it for me I think.
Again, awesome job on the new update, as usual.
EDIT: Actually one more thing. I've noticed Sleeper, that you've been trying to hangs the fleet backdrop of the boss to <fleet>battle</fleet> but it never seems to work because, like most things to do with the boss, the rebel fleet backdrop seems to be hard coded. Would it be possible though to make some custom backgrounds that include the federation fleet though?