The PCBs I had ordered from OSH Park arrived, and my co-worker Mike was nice enough to solder the components on for me. The module works, and I was able to produce 1000Hz and 2000Hz audio using FlashForth to drive the SPI signals. The sound output sounds pure and pleasant, although when I twist the volume above halfway, my ears detect what sounds like a very slight overtone or distortion, but it still is pleasant-sounding enough.
The module is a step above the usual cheap piezo buzzer circuit, the latter having the grating, distorted sound which is usually undesirable. But it is a few steps below having an actual programmable sound generator chip or a full blown sound card.
The actual PCB design here would not be used in a commercial product as it is very large for its functionality (about 6 cm wide). But it could be constructed easily by any hobbyist as the components are all through-hole and spaced far apart.
Link to design on OSH Park:
These are the trimpots that fit the board:
The GY-9833 module is also available from several manufacturers through Amazon and other Web stores.