The topic has diverged a bit and is no longer about modems, but it seems appropriate to continue the thread of discussion here....
I tried the Persist volume control app. and when the Noise Reduction option was turned off, it allowed some control over in-call volume (and also the volume of Media, Ringer, etc.) The API for android from JB or perhaps ICS ties together in some clever way the audio channels and this app unbundles them. You can 'lock' a volume level so if I lock in the lowest possible call volume before making or receiving phone calls then the phone volume is quite loud but definitely softer than before. Curiously, if I use the app to unlock the call volume, then make a call /use external speaker, then it is back to the old nasty behavior. When I go back to Persist, the call volume is blank. The app is closed source so I don't really know what is happening, but it may be that call volume is getting set to an out of range value (is this possible?) or possibly zero. So, Persist says that the call volume is zero or below while the phone application volume is maximum or beyond. Locking seems to prevent that.
I rolled back to ICS stock with a hope that starting at the beginning might fix things. Nope. The ODIN tar wipes everything so I am not sure what badness that might have occurred along the way could survive, but the rollback had no effect. An OTA brought me to 4.1.2 and a JZ build (along with a $$ hit on my data charges).
Next up I am trying diverging from stock ROMS. First stop was JerryScript's Sprintorious. This is an overlay .zip and DATA is not wiped, and so my phone is still 4.1.2 but with the Sprintorious build. For some reason this ROM has brought some sanity. The Noise Reduction option for the phone app is not there. Call volume can be modified and at the lowest setting is still loud but I can actually have a conversation. Calls in or out seem to behave the same way. What is odd, though, is that the external speaker volume is now whacked, high and distorted, and not modifiable. I will try installing Persist again and seeing what effect that has.
This is fascinating. So to be clear- you can now adjust calls using the earpiece, but the volume when using the loudspeaker?
I have insurance on my line now, so I'm considering asking them to repair/replace it, then I can experiment with a fresh unit. Not sure if it would make a difference, but it sounds like you're on to something!