Thank you Christiaan.
So to build a system that is reasonably future-proof you will need 100kbps per aircraft, 1000 aircraft over the Atlantic, total 100 Megabits.
The challenge will be to design and build a robust satellite-based TDMA system that can control and synchronise the individual transmissions. And an entirely new radio fit in all aircraft (with appropriate redundancy of course because the radio link will always be less reliable than an on-board recorder).
It's not impossible - given vast resources and general agreement from all the relevant national and international organisations - none of which is about to happen any time soon.
I think this puts the idea to bed.