Thanks to all who responded to my original post.

I did some simple digging, and yes, Sears.com has replacement parts -
but only down to the level of the "thingamajig" (actually, it's called a
"Handimate Jr.") that has the too-big belt.

The good news is that the Handimate Jr. costs only something like $25,
which is half what I figured it would cost. But I still think that
finding a 49¢ belt for it shouldn't be that much of an effort.

Any suggestions on an independent parts supplier where I might be able
to find the belt? Again, this is a belt, maybe six inches in
circumference, rubber, with teeth on the inside to drive the little
plastic gear.