I understand the handshaking requires full duplex
No you can do it with half duplex.
Aren't there programs like Bitware that will use the modem to pick up the phone, receive faxes, receive data, etc.?
Yes but as I understand it, it uses the sound card to do an input and the much more powerful processor on the Windows machine.
was just saying that the receiving part should be minimal.
But it is irrelevant how much it is used, it is the functionality you need.
It is simple enough to use minimum hardware to convert the tones into TTL logic levels and then receiving should just be the standard software serial stuff. Going to a Uno with it's crystal clock should make reception a lot more stable.
software can be used to make it pick up the phone and follow the AT commands it receives.
Possibly but I have had little experance of that sort of thing because it is illegal in the UK. Even a home built acoustic coupled modem is illegal in the UK. Everything attached, in what ever way, to a phone line needs to be "type approved" which means expensive testing outside the range of an individual.