I've never built a Stellar Balancer, so no comment.
If you want defences on your carriers, build bigger Carriers
Regarding the Shadows swatting your fighters, maybe if you had bigger carriers so as to launch even more 5 member fighter squadrons you could overwhelm the Shadows point defence. Also, try putting some armor on your fighters.
example (all figures are from Version 33)- a Shadow PDF Multiphased Cutter X at minimum range does 257 points of damage. Light Armor Class 6 absords 15 points/kT. If you put 18kT of light armor on a Heavy Fighter it will survive a direct hit (though with only 7kT left over, won't be good for much else). Putting 9kT on means that the first fighter in the stack is toasty - but the second will survive that first salvo and hence may get to fire it's own weapons.