Using sat comms is most definately possible and to return to superpilots post when transmitting information you would use mnemonics rather than words - so you mark up the data into small mnemonics so you transmit only bare information (which also can be easily compressed).
The bandwidth and the transmission are still the problems, whilst a single aircraft is not an issue if you look at the number of flights across the world at any given point you start to get a scale of the costs involved (if I recall correctly from a conversation a while ago it was around £5k per month to rent a single 64k channel on Inmarsat and that was for only a single satellite) - also as pointed out here previously such information can only reliably be transmitted when in stable flight because of alignment issues between the atennae and the satellite.
VinRouge hit on an interesting point in replicating to nearby aircraft - this is more practical due to the use of omnidirectional antennas for HF/VHF etc but it does pose some issues which can be overcome but require a global change across all fleets.
The problems are mainly that seperate portions of a FDR log could be stored across many different aircraft (i.e. an aircraft being replicated to may be travelling in the opposite direction so will be only in range for a shortish period) - these would need to be gathered together if required which would involve a logistical problem in identifying which aircraft had which data (not insurmountable). This also raises other issues such as if you have multiple aircraft in the airspace who replicates to whom and how long are they going to be required to keep it - this puts a dependency on each aircrafts FDR having enough capacitiy to store not only its own information but that of others - technology is there already to cope with this but you require all flights to be technology capable to that extent required.
As has already been pointed out the number of incidents where the FDR is not recovered is minimal to a point that the huge cost and logistics of retrofitting such a technology is prohibitive - it may be a directive one day that any new purchases work along similar lines to the above but although its out of my field I personally cannot see it being viable to retrofit.