You hit the nail on the head. I am a Spanish 21 player, and have read the definitive work on it by Katrina Walker. I get dirty looks when Spanish 21 (. . . . and so Fun 21) basic strategy varies from reguar BJ basic strategy. Like when the dealer is showing a four upcard, and I have a 12, and I hit it.
I don't think that Carnival allows a double on a double at their version of Fun 21. But I may try it, like when maybe the dealer is showing a six, and I have an Ace and a four, and then double, and get another Ace. It doesn't hurt to ask if one can double again! The most important rule in Carnival's Fun 21, though, is that Carnival allows early surrender. This can save you a lot of $$$ when the dealer has an Ace upcard.