You could also try building decoys and sending those through to drain their magazines until they're either useless or moving back to rearm at a depot.
That's exactly what his Breacher-class are no?
Yes. That's exactly why I put 30x CIWS on them. And it worked great.
Nah, I mean true decoys, not blobs of anti-missile weapons.
Like, make fighters or FACs that are basically nothing but armor and drop them through the JP. They'll soak ammunition way more efficiently because the AI doesn't have the brains to not fire full salvos at targets like that, never mind holding fire. At the TL you look to be at (and still mostly operating in Sol), nearly 4k BP represents a substantial investment of time and resources. That's mineral stockpiles and yard time that could be building up your infrastructure and fleet instead. The big blobs of armor and PD are more for when you have a foothold in a system but need to break through something like a Precursor missile station so that you can kill it and mop up whatever is left.
That's why I'm suggesting either draining them with dirt-cheap trash decoys or just ignoring the JP until you can handle it. Same general principle as leaving systems infested by Swarm/Invaders/a hostile NPR until you can break them, except more self-enforcing. My current campaign right now, I've got one chain in a nebula full of Swarm that I'm ignoring for the foreseeable future because fuck that, a system adjacent to Sol and at least one chain occupied by Invaders, two chains with NPRs colonizing in them, and a whole mess of Precursor bits and bobs. I got about 3 jumps out from Sol on every chain I had free rein in but didn't have many good basing options, so I pulled back, built up orbital defenses, threw together a few crappy task groups to start clearing Precursors, and then buckled down and bootstrapped my tech, mining network, supply chain, and shipyards to the point where I could crank out 70k ton battleships like popcorn to smash the Invaders and NPRs.
teal deer: You're in for the long haul, and resources are limited. It's perfectly okay to ignore threats that can't touch you and focus on getting the non-military side of things booming first.