Mine's a Hills Retractable, and it turned out that the job could be done without dismantling anything at all once I knew how to do it.

At the one end, the tensioning widget's controlled by a lever on the side that just needs to be shifted to let the tension off; very simple, only I shifted it the wrong direction at first and nothing happened and I tried several other things before it occurred to me that the answer might be "shift it in the other direction". (It goes toward the other end of the line to let the tension off and away to put the tension on, which is perfectly intuitive once you already know the answer.)

At the other end, the end of each line is strung through a hole in the end bar and then knotted to hold it in place. This was tricky to do when the end bar was in place, but fortunately it's designed to be unhooked when you need to work on it. (Or, I suspect from it being called the Retractable, any time you want to wind the whole thing back into the tensioning widget so it's out of the way.) I had some trouble getting the hook to unhook, since it had been sitting in place in all weathers for however many years since someone last unhooked it, but I got there in the end.