It is a voice modem (on the recommended list) with a voice driver (Unimodem Full Duplex Audio installed with the modem driver, and the Modem Line Playback shows up in the list of Audio Play Devices. Interestingly, when the Play Device in the Audio settings of the Call Test Simulator are set to Modem Line Playback, I can hear the call simulator through the phone line. IVM appears to be selecting the WRONG play device when playing the call through normal operations and not through the simulator, and there seems to be no option to fix this.
VOIP, unfortunately, is not an effective solution for my application.