North Atlantic 'Oceanic' Airspace above FL55 is 'Class A', (Below is 'Class G'), so you would therefore require an 'ATC Clearance' to operate above FL55.
However, by the sounds of it, the simplest way to conduct the operations you describe would be within an 'Airspace Reservation'. This would enable a 'block' of airspace to be allocated for the purposes you describe. Given how little traffic operates within the NAT at or below FL120 I doubt there would be much practical difficulty in securing a reservation for your purposes.
As 'Sponsor' of such an 'Airspace Reservation', say for example 100nm radius around the launch vessel, from surface to FL150 with a 5 hour duration, you would have to provide the relevant ATC provider with sufficient evidence and guarantees to show that the activities being undertaken would not exceed the limits of the reservation itself. The launch vessel would also have to maintain comms via H/F Radio or 'Sat-phone' with the relevant ATC provider.
Gander Oceanic (Nav Canada) or Shanwick Oceanic (NATS) people will be able to provide guidance as to what info to provide and how to go about it, so I suggest you speak to them in the first instance.
http://www.natroutes.glideslope.de/images/ABC.png
Above link shows FIR boundaries in North Atlantic (Disregard the 'Track' structure):
Shanwick OCA (UK/IRL); 45N-61N, Scottish/Shannon/Brest/Madrid Domestic FIRs-30W
Gander OCA (CAN); 45N-61+N, 30W-Canadian Domestic FIRs
Reykjavik/Iceland FIR/OCA to the North of Shanwick/Gander.
Santa Maria OCA / New York OCA to the South of 45N.
Rgds
T3
ps. Global Hawk and a 'Model' Aircraft are the only two UAVs I can recall transiting the NAT Region. (The 'Model' Aircraft was in 'Class G' all the way).