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If you've already printed the zero tolerance balls and they're still popping off easily (and not breaking), you could try increasing their size slightly. Dragon seven has the balls in one piece with the pieces, as I understand it, and 7Fish did these separately because of their tendency to break. You could see how many of those parts are interchangeable, or use meshmixer to combine the pieces (load the two peices, separate shells, position the ball joints, then boolean combine or make solid), if you prefer them together.
Run the string/elastic cord/wire through the holes in the peices (easiest to do if you haven't put it together yet). This dragon was inspired by Braq (https://www.thingiverse.com/thing:854575), which is an entirely cord-connected ball jointed dragon that has a video of how to put him together, it might help with this question? Every piece in the neck/body/tail has a hole in the center of the connection, run the wire/string/cord through the holes the length of the dragon (pull it tight before tying off if you're using string or elastic cord). I haven't looked closely at the hands/arms/legs/wings yet to see if they can be strung, but I believe they can be.