Thanks to Knothead's video, that is. Since I had to do the real thing on the boat with the new line already through the furler and block, I couldn't have the video with me, so I watched it a few times, took notes, and did one practice ahead.
So Friday evening I cut the old line, attached the new one to it and pulled it through the furler, which committed me to the job. My only real problem came after getting cover 1 through cover 2--I got confused on exactly where to stick the other cover in! Got a little panicky at that point, sitting there with a line with tails sticking out of it everywhere. But I sorted it out and it all worked as shown. Never mind how long it took.
BP, the times I've had trouble getting the fid through, it was because I hadn't pulled out a bunch of core to let the cover scrunch up to give space--works like one of those finger "handcuffs" that get smaller as they are pulled--pulling out a bunch of core lets it relax.
Thanks again Knothead.