The first trick to dealing with any alien, especially the Star Swarm, is scouting.
Always have small, long endurance scouts that probe at least the main planets first. Always have a sensor satellite places on both sides of every jump point. If you do discover a boojum, do not lead it out. Never transit a ship that the enemy is tracking.
If you can find them without them finding you, you then scout to find out their weapon's mix, speed and range. If you discover an enemy that doesn't have missiles, consider going for short ranged 1 MSP missiles. Yes, you will be sandpapering the enemy, but if you only need 5 million km range or so you can fire to disable, and the small launchers can reload quickly too.
If you have the capacity to blow through the shields of the mother ship, do so, otherwise, just avoid it until you do.
The problem with the Swarm, in my opinion, is people think they are a huge menace and so they go in with their whole fleet, and there will therefore be ships that the Swarm can overtake and destroy. If you only let the swarm see ships that are faster than them, they are manageable. Yes, your swarm hunters will be overengined fuel hogs that can't carry enough missiles to defeat all of the parasites, but they can outrange them and withdraw and lather rinse repeat if necessary.
If you have good information on the enemy, and enough time to retool and build ordnance, you can often have a flawless victory even at low tech level. But to do that you need that information and time.
Having fast scouts is absolutely of critical importance, because they can also buy you significant time as the enemy tries to chase them down, sometimes with their whole fleet.
Once you are absolutely certain you have killed the parasite craft, including gotten some of your fast missile boats in range to fire missiles at the mommy, if that doesn't prompt a reserve launch, THEN bring in that mommy swatters. You don't need particularly fast or accurate missiles to hit that slow ship. You just want the most warhead you can fit into 1 MSP. And you either want a huge launch to kill it in one blow, or rapid fire to peel it apart before the shields regenerate.
I ended up with a lot of different missile categories, as my missile tech advanced while I expanded my ordnance factories. So to be efficient, I made sure that all the missiles of a particular volley would be of the same type. You can also attempt stunts like firing the older and slower missiles first, then the progressively newer and faster ones, so that they cluster on target a bit.
As you start cleansing infestations, you will get a better idea of how many missiles and launchers you need to kill how many ships, and that will determine your pace of operations.
Always scout. Don't bring anything in range of sensors that can't run away. Kill bugs!
