Note that laser cannons have half the projectile speed of laser repeaters (700 m/s instead of 1,400 m/s), so the distance between the pip and target will be twice as much if you switch to cannons, and the target has twice as much time to change direction and avoid the shots. Though cannons are more efficient, they are harder to hit with than repeaters and if your gunners are good enough to do that, they'd be much more effective with Revenants. If you go ballistics you can't stay in long battles, but you will kill twice as fast, and have much more power available to shields and engines, and the Carrack needs that power.
Given the weapons are all going to have their stats changed again I suggest focus more on updating the shields (military A FR-86), the reactor to highest power and overclock during combat (Industrial A Durango) as stock power available is not nearly enough. Grab max cooling (Industrial A ChillMax) and swap the Q Drive for something faster (Military A TS-2), which if you overclock will give you excellent combat jump capability, saving you more than a quarter minute on every spool. If you are micro-jumping in combat on short notice, military matters. (Note that overclocking the Q drive does not shorten travel times but only spool time. You only need to do that during battle.)
If you optimize around ballistics, your shields will recharge much faster, your maneuvering will be much more nimble, and your guns will be much more deadly, but they will run out of ammo eventually so your gunners need to use trigger control. Use Voice Command to put everything on overclock at once, and off again after battles. This ship does not have enough power for its systems, unless you go to ballistics. Going ballistics will therefore give you a noticable improvement in shield recharge rates and maneuverability. It is also important to learn to fly this decoupled, since you will burn excessive fuel in combat if you fly coupled. In most short battles (3-4 opponents), Carracks burn half their fuel and less than half their ballistics, so don't be afraid to try Revenants. They don't seem to be the limiting factor.
I suspect you're aware that the main challenges to the Carrack are the Tally, Hammerhead, M2 and the Redeemer. You need to be very cognizant of all their SCMs, relative maneuverability, and full weapons arc threat level. At present I'm convinced the Carrack can take all its opponents, especially given its much better scan. Just you need to use the Q drive to avoid torps, and not have the HH and Redeemer cut you to pieces at close range. Make sure you orbit attack nose in so all weapons come to bear at once, and put about 50% power to front shields, 17% for all the others.
Final note if you're running a full crew and planning on military action together. I posted up the other day about this discovery that the Carrack locks down ships placed on top of the Hangar doors. It is doubtful anything placed there will respawn with the ship, but if you can find a way to quickly and reliably place a Ballista on top of those doors before a bounty mission, etc., then you can fly an Ultra-Carrack.
Apart from the obvious advantage of an extra turret compete with its own shields and power supply, the missiles are a game changer. The Carrack has no missiles and opponent pilots should know this. This means in a battle, these other ships' pilots will seek to engage you out of range of your guns. If you surprise them with a pair of Hellion VIIs, odds are the best they could do is shoot down one of them, which means so long as you can get a lock, you are guaranteed 108k points damage on an opponent. That is all full of win. The limiting factor here is whether you can share the Large size radar and sensors of the Carrack with the Vehicle size radar and sensors of the Ballista.
I would be looking to fly an Ultra-Carrack if there is any way to make it work. Important note on the Hellion VII is they have an absurdly low minimum lock range of 50 meters, so you can jump right on top of an opponent and dumbfire or lock and fire them if you like, for 208k damage. That kind of tactical surprise will kill even Redeemers with ease, and we haven't even considered the uses for the 2X4 Stalker Vs, which is another 4X40k points damage in packages the large ships cannot defeat.
How do you get a Ballista on top of a Carrack? First thing I would check is whether you can spawn a Ballista on an elevated pad, where you can back a Carrack up to the edge of the pad and simply drive the Ballista onto the top of the Carrack. After that connecting the sensors between the Carrack and Ballista would seem the next step, though I don't think that is in game yet. Failing that connect, you still have short range sensor capability with the Ballista. Odds are it can see a Hammerhead at 15-20 km. The Carrack should have 4X that range, but last I checked all Large sensors were still acting as Medium, so only 3X.
Final pitch on the Revenants: on overclock, the Revs do about 12k dps for 160 seconds. With all 8 Revs firing on one target at a time, most targets will go down in 1-3 seconds. We're talking about large ballistics that do heavy internal damage from the first shots, flying through shields unless they're Sukoran, etc. There are no Large shields that block ballistics, so far as I'm aware.
Ballistics are just better at killing targets. Yes, there are plenty of small fighters that can no longer afford to fly them because their magazines only hold 20 seconds of ammo, but the Carrack's mags hold 160 seconds when firing at overclocked = 900 rpm.
Revenants. Try 'em. You'll like 'em. in order to get your gunners used to proper trigger control, have them practice rotating the barrels by periodically tapping the trigger long enough to start the barrels turning, but short enough that the gun does not fire. If they acquant themselves with keeping the barrels rolling but not firing, they'll be 90% of the way toward holding fire when they're not on target. Twitch, twitch, twitch.