Use "coated" kevlar. Don's Hobby in Salina, KS carries it. You can get it in bulk, along with clevis's/fittings. I don't see carbon fiber being much use in this application... it's way brittle, whereas the kevlar is much like string with probably 1000 times strength, also kevlar being "non-metallic" is probably better for your signal reception.
If done right, it makes what are normally flexible, unstable surfaces, totally fixed, and rigid, a necessity in my opinion for any "flat" stab surface. Different story if there's any foil built into stab, but flat-stabs SCREAM for flying wires.
You can use aluminum tubing for your rigging, and Don's has "eye"-bolts in either 2/56 or 4/40. Harbor frieght has the "electrician's crimp to make those pro looking couplings with the aluminum tube. I'll post a pic of my set-up a bit later(when I get home).