After looking at the worldview imagery of this region in June and July of 2012 and 2016, I've noticed some patterns:
1. This ice never gets pushed north away from the coast by wind or currents. The ice on either side of it does, in the Beaufort and Chukchi proper, but right it this area on the border between the two seas it just doesn't. In fact, if anything this ice has a tendency to be pushed into the coast and replenished from the north, east, and west. Something most be going on with ocean currents and subsea topography there. Which brings me to...
2. Hanna Shoal. If you look at the region on July 22nd and July 23rd of 2012 and rock the image back and forth, it is obvious that one icefield located right near Hanna Shoal does not move along with the rest of the pack...and in fact, it never moves the entire season! It eventually melts out in September, so I doubt it was an iceberg. The ocean must be exceptionally shallow at that spot to ground a <2 meter icefield. This topography could be protecting the ice in the area.
Long story short, the Chukchi could get torched all the way to Wrangel Island, and the Beaufort ice pushed halfway across the Central Arctic Basin, and yet I think there will still be ice in this border region between the two seas well into July because that ice basically has no choice but to melt in-situ, with how the currents in the area seem to work. That said, I voted June 8-17 because this year the entire arctic icepack is mobile enough to make room for the surrounding ice to sail northward like never before, and there is less ice than ever in the Chukchi with which to replenish this area, which means we would just need the southerly transpolar winds to continue to be predominant another couple of weeks to produce something unprecedented.