Try DTMFMethod, found under Service Providers > ITSP Profile > General.
Description is Method to pass DTMF digits to peer device. Available choices are:
Inband - DTMF tone are sent as inband audio signal. <-- Only for an Obo110 on the PSNT port.
RFC2833 - DTMF tone events are relayed per RFC2833.
SIPInfo - DTMF tones are relayed with SIP INFO request.
Auto - Method to use based on call setup negotiation (either Inband or RFC2833 may be negotiated).
Since you mentioned Google Voice, also search on "early media", it's a telephony feature that GV does not support, and is the likely cause of the ring forever on the first example you cited.
BTW, what you are asking about are known as Ringback Tones or Ringback Signals. Also, I'd question if your description of "locally generated ..." signals is accurate. It's a worldwide standard that the signals are generated by the central office switch serving the number you called, there are some one-off exceptions in various countries (that deliver advertising), but in using GV for a year or so, I've never heard it use it's own ringback signals, including when making international calls.