Just to help offer you some reassurance that there are some things you can do to stimulate a better relationship, I'd like to point out a few blog articles I had written (in case you haven't already seen them):
Desensitizing Kili to TrumanIntroducing Kili to Truman and Modeling Target TrainingEarly Steps about How to Tame a New ParrotKili and Truman Share a PerchKili and Truman Share Kili's Cage TopBasically I think of this in some ways as similar to my flooding/positive/negative reinforcement technique for introducing new objects. Think back to how I got Kili to wear her flight harness by forcing her to be around it but also making it a very good experience for her. Now of course when you have two birds, it is much more complex but I think the same concept is beneficial. Except now it has to be applied twice rather than to just one bird. Both parrots are the training pupils here.
By training the two parrots together, I was able to distract them from each other and teach them alternative and better reinforced behavior. So for instance waving or targeting (rather than fighting) would produce treats for both parrots. They learn to tolerate and ignore each other and instead pay attention to me. Of course, when I walk away all bets are off. But the good thing is that the more of a safe interaction habit I can create between them when I am present, the more likely they don't harm each other when I'm not there. I want them to get so used to each other that they no longer care. For instance, Kili hasn't wrecked my keyboard in a while now. I just haven't been giving her the chance to and she got used to not being able to get to it. An even better example is how I can leave Kili's treat bowl (for training) relatively out in the open but she does not go to steal treats but does tricks to earn them.
If you leave the two birds on their own, there is likely to be a bad interaction where a fight breaks out. This leads to bad memories of each other and next time another fight will ensue. On the other hand, if you can force positive interaction always in your presence, then when they have a chance alone, they are less likely to take much notice of each other. My goal, like the keyboard and treats bowl, is to build enough habit of not being able to get it, that they don't fight under the same premise. Keep a watch of my blog as there will be many more updates about this flock interaction once Truman heels. Putting them together in the aviary should be quite revealing. Not sure if you have enough time before you have to decide but if they can get along all day in an aviary, then I think the odds of Cape + GCC are in much higher favor. I really don't know of many people with Capes and other parrots so this is fairly new ground we're breaking here.