I don't think anyone really has specific rituals for each river. That is more of a raft guide thing... The rafters tend to go to the same overnight rivers, and most of the trips have a theme for the trip, or at least different theme nights. They tend to be the more normal river enthusiasts.
Kayakers on the other hand, which is 95% of this forum, are the adrenaline junkies of Colorado that tend to drink too much, throughly enjoy a good safety meeting, and will travel all over the country just so they can huck themselves off as many different rivers and waterfalls as possible. Thus, the lack of repeat of rivers, and the loss of memory from concussions and minor alcoholism pretty much gurantee that even if we had a ritual, we'd forget about it before the next time we showed up at that river.