I have been with parties that captured a couple dozen pirates now and I have some advice. You might try sneaking up behind them. Keep firing your bow cannon and make sure they are in front of it. There are no rear firing cannons. Also the hit and run tactic does work. It is my belief that cannonballs disable their ship so you can board. Grapeshot, as in real life, harms the crew, but does less damage to the ship structure.
Having only so many shots before your own ship becomes disabled in the fight means wisely choosing what to load the cannon with. Make sure gunners each have the needed items for cleaning, loading, fusing and a match to light the fuse. Whichever gunner has the pirate before their gun fires and immediately prepares the gun to fire again, or casts some area effect spell if possible at the pirate crew, or fires arrows.
Do not bother to target the main pirate until you get aboard or you will be wasting your time. Even Energy Vortexes, armor piercing weapons, AND a Greater Dragon take a long time to subdue or kill the ‘reward' pirate. Also we don’t check anymore for the useful pirate names before we hunt. It seems that any pirate qualifies for a reward.
There is an interesting technique I discovered, using a rowboat. In just the right way you can place something that floats. like an empty potion bottle, on the edge of a rowboat and row away from it. The bottle remains afloat and you can block a pirate ship, or any ship, in place, if you live long enough. Send the rowboat in (preferably with a stealther so the pirates see no one to shoot at), and row to the pirate. Place something in the water to block their movement. then move in with your war ship. You can remain in the rowboat and cast spells or shoot the pirate crew, or return to your warship for the battle. This is tedious and only half worth the effort, but can prevent the pirate, or anyone else, from moving their ship for 2 hours, and there seems to be no way to remove the blockading item from the water.
You might bring a pack animal to haul away the pirates tons of food and metal ore and so forth after the battle.
You need to be partied and present with the quest giver at the seaport at the same time to share in the reward. The ship that carries the pirate must also be at the seaport as far I can tell. That ship’s owner does not need to be involved.