Thanks for your responses, guys, and sorry it's taken me so long to get back to this thread (busy day yesterday.)
@JimmyP - It would be pretty hard to create a test page with all the factors that are in play here, but you did clarify one important point - since animations execute at intervals anyway, there's no reason that separate instances couldn't execute simultaneously (from the user's perspective, anyway.)
@kriscahya - I'm afraid you completely lost me. Is noConflict() a built-in method of jQuery? If so, how does it work? You seem to be using jQuery() and $() as though they were separate functions, but my understanding is that they are aliases of one another. Then again, I may have missed your whole point altogether.
As it turns out, I believe I've fixed my current problem by switching to jCarousel Lite, which, although it's missing a feature that I'm going to have to hack, seems to "play nice" with my other animations. It wouldn't surprise me, though, if I run into this problem again in the future, so I'm still interested in any thoughts anyone might have on the subject.