Internal extension is set to Forward All Calls to cell phone (perhaps the critical piece of data).
The call forwarding functions properly but the parties to the call can not hear each other.
What, if anything, can be done to enhance the audio to a functional level?
Most of the time that issue is due to the "CO Line" voltage levels that could have anything to do with the UC520's disctance from your local CO (Central Office) to repeaters or pedastals in between the system and CO. I would start with the local dialtone provider and ask them to meter the analog lines and provide you with the levels and verify they are compatible with the UC520's FXO/ CO requirement. more info here: https://www.myciscocommunity.com/message/4793#4793
To get the volume levels you are after you may need to move toward some form of digital or IP dialtone, i.e.. T1/ PRI or SIP trunking.
Also check www.cisco.com/go/smallbizsupport for more info.