"Between 3.75 and 4.25 million km^2"
I took the US Navy's thickness prediction for a week from now & then drew in a boundary line for the extrapolation to the end of the melt season.
I sketched in the line based roughly on the following criteria
1) to a first approximation, ice below about 1.3 m thick on 17 June will melt out, ice thicker than that won't;
2) some of the ice thicker than that will anyway melt out if it is in the shallow water and more than 10 degrees south - this is ice on the Russian side and in the Beaufort. For example, I don't expect the fast ice in the ESS to survive;
3) some ice that is already right near the edge of the pack should also melt out;
4) ice that is heading for the Fram Strait will then melt out.
I then eyeballed the region inside the red sketch line, comparing it in size to the '80 degrees north' circle. There seems to be about as much ice outside the circle that is predicted to survive as there is ice inside the circle predicted to melt (or as land).
So my daily extent prediction for the end of the melt season is, near enough, the area of the 80 degrees circle.
I know the circumference of the Earth is 40,000 km - it was defined thus at one time. So the area of the circle (ignoring curvature effect) = pi * (10,000 km/9)^2 ~ 3.9 million km^2.
I'd give a 2/3 chance (~'1 sigma confidence level') it ends up within plus-or-minus 0.7 million km^2 of this - so in the range [3.2,4.6] million km^2.
That is my daily minimum extent prediction.
For the monthly minimum extent prediction, I will just add 0.35 million km^2 - which is the difference in the two parameters for the 2010s average (4.68-4.33) - so will choose the bin best bracketing 3.90+0.35 = 4.25. That is the bin ""Between 4.0 and 4.5 million km^2".