First of all, thanks again for all the replies, I'm sorry for not posting anymore in my own thread - I did check on the first couple of replies several times, but I didn't notice there were so many new ones below, not to mention a page 2. These are many ideas and I'm sure most of them would work, only I'm having trouble following some of them, mostly due to language issues - I'm from Germany and unfamiliar with most specific notations regarding this matter. E.g. I can't imagine what whipping could mean in this context.
A well designed wrap will be stronger and grip better than a great feast of knots and holes.
That's why I signed up basically.
Unless I'm mistaken, it appears that Bronchen-Braten has put up a new photo of the swing, which shows a reworking: It appears that he has taken a rope around the plank LENGTHWISE and has made Clove Hitches around the loops of the suspending ropes. Very creative.
I have not added any new pictures, you may have missed the bottom one the first time - these are all the old constructions from about a year ago.
I have however found a solution which will do the job, I think - it's a little similar to the solutions shown in the pictures posted by derek, somewhat combined with jc's fixed gripper layout. My construction alone wouldn't have a good grip, but I have added a simple lashing strap on each side to keep the loops in place. So far it's doing fine, hasn't moved, and I don't think it will, as the horizontal pull is not THAT great, and they only need to keep it in place additionally to the naturally occuring grip.
My very first idea was to use a metal pipe that could simply have the rope run through it. I went to several scrapyards and as it turns out, it's very difficult to get such a simple thing (one that is solid enough at least) - I could have bought one perhaps but I wanted to use what I had really, except the rope and the shackle.
Now off to the next problem: when tilted and moving at the same time, the gondola tends to wobble heavily to one side and I can easily imagine legs and other things being caught between the "cage" and the rope. That would be, well, bad. I wouldn't know a way to avoid that though. When I hand the gondola in a way that the two ends of the rope are parallel rather than V-shaped as they are now, then it would wobble less but they'd be closer together and that would end up in just as much leg-trauma-potential.
Like I said, I did a couple of complete vertical 360? spins with the old one, but only when the rest was in a "resting" position. I don't know whether I should keep that move on the schedule or not.
I did not know about the rope leverage effect.