This is really a note-to-self that may be of interest to other Manga Studio users. I spent hours trying to figure something out that turned out to be really, really simple. I hope I save someone (including my forgetful self in the future) hours of hair-pulling.
The way to preserve transparent pixels (such as those around the horse on the left) when saving to an output file is to use the PNG file format. That’s it. No mucking about with alpha channels and other such mysterious things that come up when you search for information on the Internet.