What is the gauge of that wire? If you do some reading about grounding for lightning strike, you will find so many varied opinions that you will probably not know what to think is correct. But in some of my reading, it seems that the ground cable should be at least 50 mm squared in cross-sectional area. I've also read that the cable should be no less size than 4 AWG. But 4 AWG is only 21 mm squared so 1/0 would seem to be more appropriate. Your wire looks like it is no more than 10 or 12 AWG (if that?) and I find it hard to believe that it would be there for any other reason except for "show". I know the one on my boat is about that size so I place no merit on it at all for protection.
That said, there really is no reason why you can't remove that nut, if for no other reason than to remove the remnants of the old wire. The keel will not be compromised. Heck, you could probably remove the nuts from all of the keel bolts as you are sitting in your slip and the keel wouldn't fall off. I'd bet it is bonded with adhesive/sealant (like 5200) between the stub and the keel ballast, and the studs would be bonded within the fiberglass as well. But it is true that you shouldn't replace the cable connection under the nut. I don't see any reason why you couldn't add a second nut on top and sandwich the ring between them. I agree that drilling into the square plate is impractical because they are too small for the correct sized stud and drilling into the top of the stud would be ridiculously hard to do. Why would you do that anyway? A hole in the stud would compromise the stud and make the nut completely useless for strength. Besides, why introduce more potential for crevice corrosion? If you really feel a need to replace the wire, you may as well size it correctly. You'd end up with a ring terminal for a battery stud, no doubt, which should be large enough to fit over the keel bolt stud.
The stains may not even be rust stains. Those weeps appear to come from some hidden areas. If you have any persistent leaks, which you may have given the water in the bilge, you may have some wood somewhere that is releasing those stains as it gets saturated during rain events. I know that it has happened in my bilge and that is exactly what it looks like.