You should research a level of meson focusing technology, even if it starts getting expensive.
50k range is a must if you actually intend on hurting someone with them aside from missiles.
For Beam-Weapons the options are:
Area Defense
Final Defensive Fire
Final Defensive Fire (Self only)
What they do:
1. "Area Defense" works like regular weapons, in the fire phase, if not assigned another task, the weapons will target missiles in the set range and fire on them.
This works best with weapons with a reasonable range, to actually hit something 5 seconds before it can reach you.
It works nicely when having your Missile Defense fly in front of your fleet.
2."Final Defensive Fire" fires the weapons in the movement phase, when the missiles move, and can thus be used on far shortar ranges.
The average CIWS has a range between 1000 and 60000 km, and will operate in that mode.
It is basically a point black defense and should be used with Gauss cannons and Missile defenses within the fleet.
3. Self only explains it all, the ship will only defend itself.
Feedback for your ships:
I would try to get the firecontrols have double the range of your weapons, at 50% range, they also have 50% accuracy, and thus, having a higher fire control range increases your hitchance.
As you will get only one shot, you can of course set the FDF range to 1 (10k km) and be happy with 50% accuracy.
As your obviously fighting high tech enemies, presumable [spoiler:2709qujf]Precursors[/spoiler:2709qujf], A level of Gauss technology might be a good investment aswell, as those weapons make a formidable Antimissile Defense.
I'd wait to the next engagement, research Ion Engines and a level of Armor and Meson range, and overhaul your Cruisers to be a little more speedy.
Also grants the access to missile engine tech.
What Warhead strenght did they have?
Missiles Crater Armor, so a 4 point strength missile creates this Damage template:
0XXX0
00X00
00000
More armor on your ships would make them tremedously more durable^^
If all else fails, and you really want that system rather now than tomorrow, you could build a commercial freighter (lots of outer hull) and plaster it with 10 levels of armor, just send it in and try to deplete their missile Storage.
Of course, shooting missiles down is cheaper.