Figured out one thing. The modem isn't getting the initialization string if there is an existing connection.
Easy fix:
32093 O.#2,13,0,"R:":X.36,#2,DBAUD,0,"R:":X.40,#C2,O,O,"R:":GOS.TWOSEC:?#2;"+++";:GOS.TWOSEC:? #2;"ATM0HV0X2Q0E0S0=1^M";
Replacing the ^M with a CTRL-M character.