Sort of an odd situation. At first I was concerned that it was a problem with loading two copies of jQuery, but I resolved that and my issues persist.
I tried several Nivo Sliders and liked this one the best, but it only works when I have Nivo Slider for WordPress active at the same time.
With both plugins active, Simple Nivo Slider uses the CSS from Nivo Slider for WordPress and possibly JS resources as well, and it functions beautifully. Once I deactivate Nivo Slider for WordPress, however, it breaks. The first problem is that it displays in a div with 0 height. I tweaked the CSS to fix that issue, however, and now all I'm getting is the loading gif.
So the problem, as far as I can tell, is that Simple Nivo Slider isn't loading the featured images properly unless Nivo Slider for WordPress is active. That's bizarre, though, because part of the reason that I don't want to use Nivo Slider for WordPress instead is that it doesn't even call featured images.
Obviously, the basic issue is that Simple Nivo Slider isn't loading my featured images and is stuck on the loading gif. I'm just extremely confused because it functions normally in the presence of another superfluous plugin.