I think that a great way to help spread 960 tournaments would be to do exactly what the official Lichess Swiss Team does and just set up swiss tournaments that start every 6? hours for 1+0, 3+0, 5+0, 10+0 (30+0? lol). Based on what I've seen from those tournaments the top couple seeds will always finish the event and I've already seen a bunch of reoccurring faces in every time format.
Official Lichess Swiss Team link:
lichess.org/team/lichess-swissI think that those tournaments are automated by a bot but if this is the official Lichess team then it might not be a problem to set up by someone who knows how all that works.
In fact I think that every variant team on the website should do something similar.
However if you set up 960 swiss tournaments at this moment you might not want to have as many rounds as they have for regular chess. 1+0 is 25 rounds, 5+0 is 12 rounds, 10+0 is 7 rounds, and 30+0 is 5 rounds. Setting up swiss tournaments for variants with fewer amounts of rounds would help grow the tournaments because of the players making less of a commitment.
I agree with the idea of making more rapid and classical 960 tournaments because Lichess has always had 1+0, 3+0, and 5+0 960 arenas.
We would just have to see if given the chance people would enter longer time controls for 960 and having less rounds in a swiss tournament would help people take the leap.