1. Completely unofficially I would mention that it is highly likely that someone on board would have a cell phone or similar device; and although this method might be totally inappropriate for normal ATC communications it would serve to open up a channel for some basic information exchange.
2. A recent one-off unofficial trial for data gathering was carried out on our unit with an airline with whom we have an excellent liaison process......in the event that no other method of communication was available it was possible to send an abbreviated message limited to 8 characters via the transponder mode S a/c call-sign identifier input. [This would only be of use within an area/unit that had the necessary equipment.]