You wrote, “It is thought that Arctic ice melt beyond a certain point will not regenerate.”

That’s wrong. Most Arctic ice melts every summer, and re-forms every winter, and always has. There is no “certain point” beyond which frigid Arctic winters won’t freeze water into ice.

You also wrote, “If we allow all the ice to melt, there will be nothing to prevent the arctic waters from rising above freezing.”

That’s exactly backward. In the Arctic, eleven months of the year, ice coverage keeps the water warmer than it otherwise would be. Only for about one month of the year is the opposite barely true.

Reduced ice coverage increases the rate of heat transfer from the ocean to the air. That cools the water, and warms the air.

Many people see the correlation between warmer air temperatures and reduced Arctic Ocean ice coverage, and think the warm temperatures caused the reduced ice coverage. But it is actually mostly the other way around: reduced ice coverage drastically accelerates the transfer of heat and moisture from the relatively warmer water into the air. That warms the air while cooling the water.

It is a natural “thermostat” (negative feedback) mechanism, which curbs warming of the water in the Arctic Ocean and, more importantly, at the northern end of the AMOC. It is one of the reasons that the ocean depths are not warming up significantly, and one of the causes for “Arctic amplification” of air temperatures.

You also wrote, “The main consequence of an ice-free arctic is that the blue open ocean is much less reflective than sea ice, which leads to significantly more solar radiation being absorbed.”

That’s also wrong. For about eleven months of the year, outgoing LW IR and microwave radiation from the Arctic exceed absorption of solar radiation. The main source of heat in the Arctic ocean is currents (water and air), which carry in heat from lower latitudes. That’s why the Arctic is so much warmer than Antarctica.

Ice coverage obviously does not reflect sunlight at night/winter, because there’s no sunlight to reflect. What it does do is insulate the water, reducing evaporation and heat loss to the atmosphere. Based on Nimbus-5 observations, Zwally, et al. 1983 reported that:
“…the release of heat to the atmosphere from the open water is up to 100 times greater than the heat conducted through the ice.”
Source: http://www.dtic.mil/dtic/tr/fulltext/u2/a278193.pdf

Here’s a graph, showing the Arctic radiative energy budget, at TOA:
https://www.sealevel.info/2015_lecuyer_eeb_jcli_fig8_full_sized_arctic_only01.png

The heavy black line is the net radiation flow. As you can see, it is negative about eleven months of the year, which means that the Arctic is emitting more (longwave) radiation than it absorbs (from sunlight).

Source: L’Ecuyer, T. et al, 2015 (or here). The observed state of the energy budget in the early twenty-first century. J. Climate, 28, 8319-8346. Fig. 7 & 8.
http://dx.doi.org/10.1175/JCLI-D-14-00556.1

An “Arctic Blue Ocean Event” would open the Northwest Passage to shipping, but would have few other consequences. Because more open water would increase ocean evaporation and thus “lake-ocean effect snowfall” on nearby land, it might decrease the rate of sea-level rise slightly, and add to Greenland’s ice sheet. But that effect would probably be slight.

You can read more about this topic here:
https://sealevel.info/feedbacks.html#seaevap

You can learn more about climate change in general from this list of excellent resources:
https://sealevel.info/learnmore.html