I think I'd use 2 or three fire controls. You have 5 turrets with tracking speed 12 and rather short range (fine for PD, less so for fighters if they use anything but gauss or a lowtech railgun. I doubt anyone uses plasma carronades.), damage will drop to 1 pretty quickly, so even against fighters you definitivly need a couple of hits if they aren't right on top. In that case your to hit is lowered as well.
I was gonna say something about only 3 layers of armor, but then I looked again and saw those shields.
I'll need some as well. There are about 100 enemy AMM launchers at a planet I want to invade. So it is either multistage missiles (which release as many size 1 missiles are possible about 3m km from the target) and lots of them, or better PD (I had 20 each of regular sized and 50% sized 4-shot gauss in 16k tracking speed turrets and about 45 railguns with ~7k tracking speed. Not nearly enough.) coupled with shields to break through to beam range. My next gen (magneto plasma) fleet will do about 9500km/sec, so they are basically standing still for the 70k km/sec missiles.
Edit: Wait, you have strength 10 shields that take 300 seconds to recharge. No, that is mostly useless I think, at that stage I'd invest the tonnage in armor. Your shields can take about 1 1/2 of the usual spoiler missiles, 2 1/2 if they use rather small ones.
Editedit: Your FAC has 2 missile launchers, you'll need a lot of them to break through any missile defence. They won't operate far from a base anyway, so you could try and see how many box launchers you could cram in instead to increase throw weight. And if the defence isn't that strong you can just use one or two of the FACs at the same time, or use them to engage multiple targets.
All your ships are rather slow for internal confinement in my opinion. My ion engine fighters go 8500, the magneto plasma ones will do 13500km/sec (I researched a higher engine power modificator in the meantime as well).
Line ships in my current campaign have more than 50% of their weight devoted to engines, though that is faster than I usually go. Normal for me is about 40% of the weight.