The narrowband profile also works, but I needed to create a new Quiet profile with a center frequency of 2200Hz.
Compression is going to mess with the signal somewhat, and encoded data is not particularly alike to the human speech that most psychoacoustic models are aiming for. But you can get modems to work across some quite poor connections if you keep the bitrate low.
If you don't need to send a bit-accurate binary blob across the network then it's much faster to use such analog modes and accept some corruption. If you wanted to send a picture across a noisy radio network (as emergency-service operation tends to be) I would actually suggest sending a radiofax or a slow-scan TV signal. Lossy compression would distort the picture but the human brain is quite good at dealing with this kind of distortion. This is particularly true of faces - the brain is wired to match faces quickly, which is how we get pareidolia.
https://en.wikipedia.org/wiki/Slow-scan_television
https://en.wikipedia.org/wiki/Radiofax
During WWII the Germans actually used a mode called Hellschreiber that basically sent text as a B+W fax picture, with each line sent twice for resilience. It's not the fastest but it was quite resistant to interference. It's interesting to think of modern improvements we could make nowadays.