Do you think the results would be different if they started at June 28th ??
No. I worry that the model used to claim no evidence for hysteresis has a heat sink that is not properly accounted for. The most current estimates for the first ice free Arctic cited by the IPCC itself confirms this heat sink.
If I had to chose a starting date it would be at the beginning of a month.
If I had to chose a starting date for maximum perturbation I would have chosen as far back in the melting season as possible to capture maximum solar power. If I would have chosen July 1st an almost random, "good enough" date I wouldn't have called it Maximum perturbation.
Also you are using DMI 80N a real observation as an argument about a model. Do you know the models equivalent DMI80N metric?
DMI N80 represents an extremely small horizontal surface area in 2D and just the surface right above the ice in 3D. It does not represent anything above, below or south of 80N.
However, it also represent the coldest place in the Arctic. It starts taking solar energy after everything below it and the sun stops shinning there before anything to it's south. It is also adjacent to the last great ice sheet in the North Hemisphere, Greenland. Not to mention it is sitting right over some of the deepest waters in the world.
If there is anywhere were refreezing should start in June, is there. However temperatures are at maximum in early June, in the coldest place in the Arctic. The only place where freezing takes place in June is the ice healing itself. But there is no ice to heal itself.
In the real world of today, if all the ice is magically removed in June the ice will not return until November, probably longer.
Can you see the future? How do you know 2070 is 20 years too late? Why not 25 or 15 ?
From the IPCC, according to crandles' post above:
In particular, the relationship between Arctic sea ice coverage and GMST was found to be indistinguishable between a warming scenario and a cooling scenario. These results have been confirmed by post-AR5 studies (Li et al., 2013; Jahn, 2018), which implies high confidence that an intermediate temperature overshoot has no long-term consequences for Arctic sea ice coverage.
I checked Jahn 2018 because it was the most recent and I found the attached graph. RCP 8.5 leads to an ice free Arctic much sooner than Tiesche et al predicts. This is proof that there are heat sinks in Tiesche. The models used to claim no hysteresis are running cold with respect to the Arctic ice.
If there was a threshold behavior change the heatsinks in the models are likely hiding them, like they hid June warmth.
Even with the heatsinks we get several years of memory.