On the premise of: “These pirates are your people, YOU deal with them, or we’ll deal with them for you.”
Each ship should carry a large trebuchet. Capture the pirates, sail within its aiming distance, and send the pirates back, one by one. Here’s hoping their screams are an adequately heard message.
Alternatively, execute them once captured. Mount their heads on spikes lashed to the rails of the foredeck of the ship, then sail to their country’s docks. Dump the bodies in the water unceremoniously, and sail off. This might require a naval escort; all the better.
I’m not sure about this plan ... going after the ringleaders might mean some arrests in Saudi Arabia and Europe. It’s not such a stretch to see that there is somebody pulling the strings behind the scenes, for power or for politics (duh, that’s the same thing innit?)
Kill them all, sink their ships, leave no trace for their families, just make them vanish from the earth. NO exceptions, NO mercy.