So it turns out that the transformer wasn’t necessary. I broke out a pocket oscilloscope, and it boosted the voltage from 1.5V pp, to 7.5V pp, and the resulting volume in the earpiece was VERY LOUD, so I tried without the transformer, and it worked perfectly, and at a much more reasonable volume with the alsamixer controls on the computer set to mid-range.
Since that worked so well, I decided to try hooking the phone’s mouthpiece/mic straight up to the mic jack, and that worked like a charm as well. I was able to play the game with only a few problems with the STT engine due to slightly noisy input. I think I can tune that away using alsamixer again.
Lesson learned. A standard, cheap sound card/dongle is capable of interfacing with an old phone directly.