I think the summer period volume estimates may not fully incorporate the fact that the nearer one goes to the pole in the summer, the circular reach of sunshine prevents permanent and semi-permanent shadows that keep ice cold preserve it longer.
In June the north coasts of Greenland and Ellesmere (often cited as the last "sea ice refugia" for the last 1,000,000 km2 where sea ice would survive) to produce a plateau in melting or be linear gradual phase out tail.
In summer volume, I think it is rubbish this idea of 1m km2 of "sheltered ice"(!) Even though, there are mountains in Greenland / Ellesmere, the sun still shines in these areas at 17 degrees high - creating rather limited 'shadow-refugia' by topographic silhouette (whatever it may be).
The (wrong) idea by juxtaposing the corner of the south-west Ohotks Sea sea ice refugia is a wrong comparison as that site locates so far in the south. The same applies to the little more northern west-of-Kamchatka Peninsula sea ice refugia, sheltered from the morning sun and easterly winds by the shadows of mountains in the east over the Kamsatkan silhouette. During the night, the sun is here also beyond the horizon.
But, nay, north of Ellesmere and Greenland, the sun is just about everywhere to warm the ice 24 hours (as long as there aren't clouds to mask it, and any deep sided narrow fjord excluded).
When it comes to the winter-time ice, the most important overlooked consideration for the 'cold sink' of the Arctic is the transmission of residual heat elsewhere (from the mid-latitudes) as in the Far North itself the sun is just missing totally.
As the surface area of the globe between 80 and 90 degrees is many, many times smaller than that between 0 and 10 degrees at the Equator, all I can think of, is that the tiny caps will respond (fill up their reservoirs of cold air by heat) will happen really quickly in the end that will surprise many. In Antarctica this process will eventually be even faster than one in the north as the free airspace over Antarctica's ice does not have mass like the Arctic polar air mass has (as the air column extends right down to the sea level and also interacts with surface waters of ocean).
Land ice in Antarctic is more insular than sea ice / sea water, so despite the massively bigger thermal inertia within its ice domes, the thermal inertia of air over Antarctica is much smaller. The land sitting ice there remains much more inaccessible for exchanging heat than on the North Pole as ice there cannot mix heat much vertically like ocean (although moulins and crevasses mop up water and heat once melting starts there properly).
Any variation in the anticipated winter-time retention of sun's heat is one contributor determining how much sea ice volume survives the winter, the sea ice breaking and vertical mixing and moisture (fog, low-lying clouds) will determine how much ice volume is left. The winter darkness on the poles is fixed and predictable, winter is winter always there! So, the transportation of heat in, colness out, sea ice breakage and mixing into sea water determine that there will be a quick flop at the very end of polar sea icecalypse.
The global sea ice volume would be influenced in Antarctica by meltwater and ice run-off changing sea water temperature and salinity.
Small, perhaps unfair question in bad english : I don't think it depends too much on the icefree part, as it does on how much open water for how long. If this year gets more open water than last year and for a longer time, more heat will be stored in the water. Also, how many clear days will the Arctic have this year? The last freezing season was a practical wreck from the heat stored in the water. At this point, the coming freezing season and final volume(made up of mostly FYI) cannot help but to reflect what will happen this summer.
If we would see an icefree arctic in a few years, what do you think how much volume first year ice could be generate in one winter season? 10000, 15000 ?