Thank you, LazyPup, for the detailed instructions. A return to the hardware store resulted in the purchase of a flexible PVC p-trap. Its combination of metal washer and various-sized plastic compression rings made a pretty good fit on the tailpiece. As for the troublesome ridge on the waste arm, we ended up just sawing the pipe off right above it.
The assembly isn't the sturdiest fit in the world (as there aren't any threads on the existing pipes to grab), but it holds and does not leak. Good enough.
