One possible solution:
Get a free VoxOx account. In the VoxOx app, go to Phone Setttings. On the General tab, uncheck Personal Assistant, Call Screening, Present Incoming Call Options and Dead End. On the My Phones tab, check Find Me and only one Call box, set up to call your mobile phone. At this point, you should be able to set the OBi to bridge to your VoxOx number, instead of your mobile. VoxOx will now play ringback tone to the caller, during the setup time to your mobile.
If desired, you can replace the ringback tone heard by the door caller with a spoken message, by recording or uploading it on the Ringback and Hold Music tab.
There will still be a considerable delay before the caller hears the message. A big piece of that is the four second delay while the OBi waits for caller ID information on the Line port. If that's not required (by any non-doorphone incoming uses of the Line port), set LINE Port->RingDelay to 0 in the OBi.
You can save a little more time by using iNum instead of the VoxOx PSTN number. Get a free iNum at VoxOx. If one of the service providers on your OBi does not charge for iNum calls (e.g. Callcentric,
VoIP.ms), just use them to bridge the call.
Yet faster, a gateway to iNum directly, e.g. AccessNumber: SP2(sip.inum.net;ui=12125551212;op=ns) . The SP1 or SP2 chosen must use SIP, and you must have a STUN server configured (however, you need not use STUN for SPx). The caller ID will be spoofed with whatever you specify in the ui field and will display on your mobile phone, so you will know that the caller is at the door.