It's been a while since I've touched electronics, so bear with me :)
Since I can not attach DTMF tones to an on-going phone call (https://stackoverflow.com/questions/16949867/unable-to-make-a-call-from-service), I had another idea.
If I modified a set of headphones (that have a microphone), would it be possible to directly output the speaker audio from an earpiece to the microphone and get decent results playing DTMF phones from the phone?
Android has a buit Tone Generator, so I can play DTMF tones to the sound output programmatically.
If I have to, I can fallback to SMS, but I'd have to have more logic in place for managing the 5% failure rates.