With more complex syncs, I believe a limited improbability analysis is best. I think we can present compelling floors in many cases.
I think the best approach is to to establish a general floor, a very conservative measure of aggregate improbability. Anything beyond that is diminishing returns, since we can't really establish a final level of improbability when it comes to syncs that have multiple meaningful associations. Beyond that, I think the best approach is to seek replication. Some events are especially well-suited for such an analysis, like soccer goals, since a soccer goal is a soccer goal is a soccer goal. There is much for would-be skeptics to use for comparison's sake, if they dare to. But as I said, I see two components in this test. What are the odds AND what do the odds connect to?
That aside, you raise another nuanced point here. Now that I've looked at various web sites devoted to the subject, I am left with the feeling that a lot of people don't want to know what the odds are. They see their personal experience of synchronicity as non-random and, noise notwithstanding, the real syncs likely are. If they want to post pics and like pics that show digital clocks showing 2:22 and 1:11, God bless them.