Crandles, the increase in heat transfer from the ocean to the atmosphere when ice is thinner does not "net off" in terms of heat in the atmosphere. Yes, most of that heat eventually radiates out to space but before it does fall and winter temperatures in the Arctic are pushed upwards. The effects of less ice in the Bering, Chukchi and Beaufort seas have been pronounced over the past 5 years in Alaska. They have had several extraordinarily warm winters and late falls.
The ongoing build up of heat in the summer water layer in the Chukchi and Beaufort seas indicates that there is carry over from one warm summer to the next.
Obviously, the researchers simplified the problem so we should be careful about overextending the results, but your criticism misses some key issues about the build up of heat in the Arctic ocean/ice/atmosphere system.
This and then in case of open water and considering the water was not open for just a few days in it's entirety, there is quite an amount of extra heat previously accumulated in the water and starting temps can be significantly higher, even much higher the more south or north, depending.
That means that a lot of this extra heat-loss will be extra-heat, means that part will not have an impact on the net balance but will have a significant impact on freezing onset in wide parts and that will influence the maximum thickness at the end of the freezing season and therefore impact the following melting season etc.
I think that this is part of what we are already able to observe during the last few years.
Last but not least there will be A LOT more moisture in the air and that again will impact the heat loss negatively for ice building and thickening.
Open water means oceanic climate and ice-cover yearlong means a dry desert in winter.
After all it will/does most probably depend on the relation between open water and remaining ice cover, kind of a tipping point, could be a soft tipping point instead of sudden death and the likes.
IMO we are exactly at that tipping point, slightly more and slightly earlier open water and
the system will topple towards a significantly different system. Which exactly i can't tell
could be something we know from lower latitudes but could be something entirely new.