Sadly, there's not much beyond the Alafia event that I've found.
There are some clubs that throw small events, and St. Augustine has various larger events too but some are more Pirate and 17th century themed than others. I wouldn't really refer to them as rendezvous.
Not a vous, but if you are interested in being a spectator at a reenactment, this Seminole War event is this weekend.
Big Cypress Shootout Seminole War Reenactment
www.bcshootout.com/”Ž
Seminole War Reenactment, Historical and Cultural Displays Highlight the Big Cypress Shootout - January 31, February 1-2, 2014. Friday, January 31, 2014 .