To get an idea how much ice has left the Lincoln sea into Nares strait, I have tracked some floes back to the 12th when they were at the position they had when the ice arch broke.
At a very rough guesstimate of area, that is a triangle with sides of 140km. That works out to around 8500km^2. The last image in the sequence is 27th May, so that is 15 days of export.
Therefore export rate is around 550 km^2 per day. That matches well with my original estimate of 500km^2:
Looking at the export over the last couple of days at start of the Robeson Channel (see gif) I estimate about 500 km^2 exported per day
I meant to do this earlier myself: the area marked with a thin yellow line on an overlay of 9th and 14th May measures 9670 km
2 , so your number is a pretty close underestimate.
Although the daily rate is probably correct to allow for another day or two to let the whole marked area pass into Nares strait.
If I take the Lincoln sea as the area below a line from the northern tip of Ellesmere to the northern tip of Greenland, then that area is 4.8 times that. (43600km
2) That means it would be cleared in about three more months of going at the same rate. Just to put this into context, lets see what happens.