I think your calculations are oversimplified. Low starting value years are harder to melt, so lead to lower melting. There seems to be a correlation between (potential) melt and starting volume.
Oh, no doubt, you cannot melt ice that isn't there. There certainly will be an affect there, which I think likely will also be correlated with where the ice is located. We've discussed for years where we think the last bastion of the ice is located. To summarize a lot of those discussions, the consensus was that it would be immediately north of the CAA, and possibly tucked in next to Greenland in the Lincoln Sea.
And my calculations aren't over simplified. To a greater degree they haven't really started. Beyond simply saying that I think that a 2 sigma melt is no longer required to get to under 1,000,000km2, I'm still forming hypotheses and trying to figure out what numbers to dig into next.
(Edit)
Put more succinctly, the energy for a 19,000km3+ melt already exists in the Arctic. As the end of season volume declines, it becomes increasingly likely that the energy present will in fact crush the pack. The devil is in the details of where the ice is located, and whether or not the heat can reach it. That's where I'm directing my investigations.
Key however here, is what ice is present at the end of the refreeze, which the trend shows categorically is declining at 250km3/year more or less. It's that starting point which will determine whether or not the pack survives the melt season. in 6-8 years, I think it will render what happens in the melt season moot.