Recommendations:
1. Build two sets of cannons. The first with a full 100% compliment of Cannon blocks. The second should have between 75% and 95% of the number of Cannon blocks as the first. Link the second set as slave to the first, full set. You now have a quick-fire (not quite rapid-fire) cannon. It'll do less damage, but have an easier time finding the target. Depending on how many cannon blocks you use per cannon, it can be quite effective at dropping the enemy shields.
2. Don't forget shield rechargers!
3. Have at least twice as many shield storage blocks as you have shield regenerator blocks. I find with all the twisting and turning that both I and my AI opponent do, they are shooting at one turret for only a short time. It's more important to me that the shield have a lot of points, as opposed to recharging quickly.
4. If you make your own turrets, it may be kind of ugly, but make sure you build them up in the Y direction to fill out the available turret docking cube. Empty dock space is less space for shields.
Miscellaneous non-turret recommendations:
1. Make small, insignificant ships available for pirates to buy. Not all pirates have the means to get even a lowly Isanth. With an odd mix of weaker fighters and utility vessels, the pirates now strike me as being more like a band of rag-tag misfits and outcasts who use whatever craft they can get their grubby hands on. It adds more flavor to the pirates, and there's a certain pathos when I have to blow away my own ultralight freighter design. Plus, the friendly trader faction now gets that ultralight freighter, and that just makes sense to me that they'd use that.
2. Be careful about adjusting default configs. If you make the AI too accurate, you have to expect them to drill through to the central target quickly. Likewise, be careful about leaving the difficulty on the default "Hard" setting. I'm keeping mine on easy and medium until I make a satisfying capital ship with lots of big turrets. I'm taking my time.
3. Don't be afraid to go smaller. It may be more effective to build a smaller, lighter capital vessel, so you can twist and turn around faster, spreading the damage to different sections of your ship, and to different turrets. A damaged turret is still in play, but a destroyed turret won't do you any good. With a lighter vessel, I can bring my main weapons to bear, attacking smaller, less lucrative targets first, saving the juicier targets for last, so I have time to plunder the wreckage after the last pirate is sucking vacuum.
4. If nothing else, reduce your main-vessel weapons to lighten your mass, and allow you to turn faster.
5. Be prepared to run from significant numbers. Maybe try to keep one or two pirates in range, chasing you, to pick them off and then return to the main group to wipe them out.
6. Backpedal!
7. If your ship shields are not getting dented, maybe eliminate some shield blocks to lighten your mass, enabling faster turning.