Ooh, that looks like !fun!, all right.
Unfortunately, there's not a lot of subtlety or trickery I can think of that will help. Best plan I can think of would be to first capture the CS-A world nearby. Yes, this will put the Core World on alert, but that's an inconvenience, not a disaster. If you have the spare Knowledge and you are willing, you can put a Warp Jammer station on it.
Step two is to load up Assault Transports and perform repeated suicide runs through the three Core Worlds, trying to kill as many Tachyon Guardians and the like. Once you have a clear path for stealth units, use the Assault Transports again to run a fleet and some colony ships past everything, and capture a world on the other side. Either the CS-D one you already see, or one of the next three (two hops further in).
Once you have a beachhead on the other side, life becomes easier again.
If you don't have, and cannot afford, Assault Transports, you can try to make do with Cloakers and normal Transports, but they have a much shorter range, and your options for activities on the other side will be much curtailed.