I'm almost sure that the problem is that I left something out, but I'm not sure what. You see, I didn't create the original skeleton, I just added arms to it. The skeleton I used was "2001 Skeleton.mdl," the one included with the Animation Master program (at least, version 10.5, which is the one I'm currently using). As best I can tell, the two arms included with that skeleton feature five bones: Bicep, Forearm, Hand, Arm Steady, and Arm Hinge. The new arms feature Bicep, Forearm, Hand, and Arm Hinge, and are located beneath the original Shoulder in the heirarchy. I'm not sure exactly what Arm Steady does, as my only real resource in this is the tutorial book that comes with the package and, needless to say, it's missing a lot of key information.
In this post I'm including a picture excerpted from the animation (with bones visible), with the character in question Yama speaking to another character, Yudisthira. The upper arms are the ones where I added bones.
Just as a side note, all of Yama's body parts are two-dimensional, except for his crown and sarong (clothing). This is so as to replicate the look of a Balinese shadow puppet show, which is what the animation in its final form is designed to resemble.