I'm using the jammer instead of going big guns. Big guns are never big enough when you get swamped with pirate ships. It's fun, but going the jammer route is less resource intensive.

In this run, my ship now has 6 PD guns with 3 on each side of the shuttle docking port. The pirate shuttles are all being shredded when they attempt to board. The pirates usually fly off to their ship in their spacesuits instead of boarding. This is not a good thing.

Had they boarded, they would have been killed in my kill box. More pirates in more shuttles would follow and they would be killed too. Eventually their ships would become near empty or derelict and easy to plunder.

With this 'shred the shuttles' method, all of their shuttles are destroyed to the point they can't make any more shuttles and the pirates are still alive. I'm in a pirate system and every pirate ship has no shuttles now. Maybe 10 ships.

One might think that they will run out of water or food or fuel, but they don't seem to. So you have to go to their ships and hopefully get lucky in a firefight.

I'm going to dismantle the PD guns near the docking port to get my strategic leverage back.
I hope this will help someone else. I should add that I have a one shuttle ship on purpose to try and minimize things. It's great fun to try a new approach in the game.