What I do when I make these interconnects is to twirl up the braided copper a bit, then fold it back and over the outer black jacket. After that, I will be sure the center conductor is stripped a little, slip that into the RCA plug, then check the position of those cable clamps built into the plug.
If the clamp position looks good, I will crimp them onto the braid/cable really pretty hard, usually with very large pliers. I will clamp down on hard enough that the cable clamps bite into the cable a bit, and won't come off without a lot of motivation. As far as soldering goes, at this point very little is needed, and the hard crimping will give you some control over keeping the shape small enough for the connector to fit back together.
-PB