Actually, I don't think the attraction ever took itself too seriously. Perhaps the initial idea of the Jungle Cruise was going to be slightly more serious as Walt originally wanted live animals (an idea quickly abandoned as it was realized they would always be sleeping when guests were around), but even a book about Disneyland from 1964 quotes skippers saying such classics as, "Keep your hands and arms inside the boat - these crocodiles are always looking for a hand-out." And, "Gentlemen, if your mother-in-law is still aboard you've missed a golden opportunity." Also, Animal Kingdom had nothing to do with Jungle Cruise being self-referential or comical. If anything, Animal Kingdom is what Walt originally wanted the Jungle Cruise to be...they just didn't possess the know-how to do it back then.
As for the movie, I suppose my only real fear is that they'll do with Jungle Cruise the attraction what they did to Pirates of the Caribbean the attraction and we'll get stuck with out-of-place audio animatronic characters who totally change the plot of the attraction. Yes, I know, there really isn't a "plot," per se in the Jungle Cruise, but I really don't want them fudging it up by adding "the wisecracking hero" as an audio-animatronic here and there throughout the scenes to try to link it to the film. I think the Jack Sparrow additions to Pirates of the Caribbean (and the subsequent plot changes because of it) were unfortunate and unnecessary, though I'm sure many disagree.
Here's hoping they at least do a good job on the movie.