I'm sure I'm missing something obvious here, but I want to control the active pane on a carousel by some buttons embedded within the carousel itself (mostly wanting to use the component solely for the nice slide transitions). I've got the buttons/messages/etc setup so that it changes the activePane property, and the carousel changes to correct view, but it no longer has the slide transition, it just abruptly switches. It seems that animation only triggers when using the dots/arrows... is it possible to get the transition animation while changing activePane via scripting?
Thanks!
Not at this time, no.
The problem with attempting to transition from slide A to slide X is that there could be many slides between A and X, and the component could easily run into issues when trying to transition across many Views in a relatively short amount of time. Singular Views are easy to transition to because they're (very likely) already in the DOM - the component just slides them from being out of view into the viewable area. Imagine trying to quickly slide across fifteen Views in one second as you jump from pane 0 to pane 16; that would not be a good experience.
I swear I was being good and only trying to switch to adjacent views at any given time! 
Makes sense though. Is there an approach you'd recommend for nicely transitioning between one view an another outside of the carousel?
Version >= 8.1.22:
Use the stylesheet.css resource to build a CSS animation/transition and replace the Carousel with a Carousel which contains only a Flex Container full of Embedded Views. Supply the classes required for your animation to the Flex Container as you move it left/right.
8.1.13 <= Version < 8.1.22:
Do the same thing but in the theme files of the Gateway.
That's it - those are your options. The Carousel does a surprisingly large amount of the heavy lifting for you, and while it's unfortunate it doesn't cover this use-case, implementing the functionality yourself outside of the Carousel will not be easy.