I can't accept your assertion, the Atlantic waters flowing north shed most of their inertia/kinetic energy in Barents and the Kara. All the graphics and studies i've read show the southbound cold waters gathering in the Greenland sea, with a little input flowing out at depth through Fram and a larger contribution falling off the continental shelf between Svalbard and Norway, but mostly it appears to be 'created' in situ. Also it's implicit in the explanations i've read that energetic content is fully transferable between heat, kinetic and potential energy, so I imagine that somehow it's reflected in the molecular or atomic state of the actual material.
As the ice passes through Fram and is driven south, it clearly 'wants' to head west [according to accepted theories] but can't because of Greenland, it's also moving away from the axis of rotation on a great arc so i would expect it to be far from equilibrium, and I suspect in energy deficit. The currents heading north have the opposite 'tension' leading to all the complex vortexes along the coast, which serve to refine, differentiate and resolve the potential energies present. Somewhat like the EKE in the Labrador sea.
This still doesn't resolve the question though, does ice[NH] cool as it moves south? and warm as it moves north? that is does it find itself with a potential energy deficit/excess. This would help to make sense of this summers cooling, even as the ocean was exposed when the ice was pushed apart. It would also help explain why the HYCOM CICE so often shows ice growing suddenly thicker when atmospheric conditions don't appear conducive.