This thread is heading for banishment to Tech Log, so I might as well contribute to its demise.
The kind of data the FDR records is called State of Health data, on spacecraft at least. It is generally boringly repetitious and compresses nicely (losslessly, of course) sometimes using algorithms that insert values (for each channel, or parameter) only when they change by a meaningful amount. More dynamic parameters may be recorded by inserting differences between consecutive values into the data stream, each difference taking fewer bits than stating the whole value would. There's a popular silicon-based encoder (popularly called Rice encoding after one of the designers) that choses the best algorithm on the fly, no pun intended. And all this stuff exists in boxes with 1553 interfaces, since that's become popular at higher altitudes, so to speak.
I don't look at FDR data so am guessing, but would be pretty surprised if 10:1 compression wasn't a piece of cake. The costly bit would be making the box and uplink robust enough to survive a nearby explosion long enough to deliver the last message. While the normal data rate would be low, a serious event would generate full values for each parameter at the system's normal sample rate, for the duration of the event, and that would have to be preserved and uplinked perhaps over a period of several seconds.
CVR data needn't be lossless. I have nothing special to contribute in that arena, but we all realize that a minute of good-fidelity music becomes something like 1MB of mp3 data. Voice quality would be much less than that. As with FDR data, in normal flight there would be next to nothing to send.
I know nothing about what happens next, but note that Hughes and others operate geosync spacecraft with transponders dedicated to providing internet service to hopefully more than 500 customers (cited earlier as the number of transoceanic flights in some area). They're happy to support megabyte data rates for their users - far greater than needed except for mayday situations.
Afaik no such service exists in the right place for oceanic monitoring, but that doesn't mean one of the maritime birds wouldn't mind providing such a capability. Hughes gets around USD80 per month per user, btw, and per the TOS doesn't appear to get annoyed until users start using hundreds of MB in a short period. I'm assuming that uplink and downlink are symmetrical for them, unless they do a lot of common-data caching on board the spacecraft. That's unlikely.
What to do with the data seems to bother people. Clearly the system would be operated by a central authority like ARINC, who could simply store it in a disk array at the satellite ground station - a giant FDR.
The thing I haven't mentioned is the uplink, because I truly know zilch about that. Hughes/Directway uplink antennae tend to be dishes around a meter dia, I think.