I think you've generally overdone the drawbacks.
Just as an example, I built this ship to see if I could make mixed lasers work:
Then I "downgraded" it to stock:
The stock version is 9% cheaper and wins decisively. The expensive and power hungry mixed armament simply doesn't match up to stock laser blasters. And that's with the handicap of having the strictly superior plasma reactors.
Okay,maybe the IR lasers are just bad. Let's swap them for more UVs to drop shields for the plasma blasters.
Nope, The cheaper stock version still wipes the floor with it.
The higher tech weapons tend to not be worth carrying a very expensive waste of space bridge. The iridium lasers are worth the frigate bridge, but above that? The PP1 has an iffy niche even if you're already mounting the tech buildings for other reasons and the PP2 isn't worth the bridge upgrade. The Ion Missiles don't turn out to be all that good in practice because standard missile explosions damage parts behind shields and they don't. The LFC1 costs an extra 18 tiles of very expensive waste space and I'm not convinced they're really better than large cannons for finishing ships with broken shields. The battleship stuff is just too big for shields. Here's a comparison of shielding a large cannon wall or a Vulcan wall:
The stock cannon side has 50% more shields. At this length it does 11952 dps against shields and components and 5976 against structure. It has penetration 5 and starts fires. The Vulcan side does 12000 dps against shields and components and 9600 against structure. But in a fight between the two walls it's not the structure damage that would matter. It's the nearly equal shield damage and the 50% cannon wall advantage in shield HP. And even that doesn't tell the whole story. Because of their deeper hitbox the centers of the Vulcans are only covered by a single layer of shield while the entirety of the cannon wall is covered by a minimum of three layers. The cannon wall at this length is 343,600 credits. The Vulcan wall, excluding the cost of the battleship bridge, is 500,100 credits. The cannon wall is 2 tiles thicker and weighs more than twice as much, but the example thruster block is only 60,050 credits so the cannon wall can afford more than four more of them per 24 tiles of wall.
The Vulcans are stronger, but they're only significantly stronger against armor and the inability to stack shields effectively really hurts them. LABs would fare slightly better in this sort of comparison, but require even more large and expensive tech rooms. And I'm not sure you get enough power for them through just two doors. They might have to drop in density, which would put them at approximately the same damage as the large cannons again with more range, but weaker shielding and a smaller budget for engines.
I think this mod just needs better propulsion and shielding (longer radius, not more efficient) teched off of the main engineering and warp core to offset the bulk of the battleship guns and the internal volume tax of the tech rooms themselves.