Reflection of sunlight at both poles is highest during each poles warm months.
When the sea ice in the north breaks up, it is trapped there by land in the colder latitudes and continues to reflect. When the sea ice in the south breaks up it moves away from the pole to warmer latitudes, melts quicker, and reflects less ice.
The reflection of sunlight from the land ice in the north is about the same as in the south
The Arctic Sea Ice Problem is Actually Worse-Not Better-Than We Thought
The Arctic sea ice - once disbursed by winds in the summer from a packed mass into sections - is swept by currents and the prevailing winds through the Greenland-Canada straits (and some down the east coast of Greenland) into the north Atlantic. Where all of it promptly melts.
Your claim that it is trapped and continues to reflect is dead wrong. Once ANY arctic or antarctic sea ice reaches an area less than 15% covered, the satellites and surveys reject it and it is NOT included in ANY report as “sea ice”. It is NOT continuing to reflect as you claim.
Worse - from your argument's sake - is that Arctic sea ice through its summer melting season of longer days of sunlight - is exposed to a daily top-of-atmosphere sunlight levels that are MUCH LESS than the Antarctic ice. Earth's sunlight reaches its MINIMUM of 1320 watts/m^2 July 4; its MAXIMUM solar radiation is January 4-5 at 1410 watts/m^2 occurs near the maximum of Antarctic sea ice extents in mid-February!
(Today, near the Arctic minimum sea ice extents and Antarctic maximum sea ice extents, BOTH POLES receive the SAME top-of-atmosphere radiation. But, as mentioned above and which you kindly ignored, the Arctic sea ice edge is at latitude 80 north, the Antarctic sea ice edge is at latitude 59 south. The Antarctic sea ice edge, now at record high levels, is receiving 5 times the radiation each second that the small bit of Arctic sea ice is getting.
Worse, the arctic sea ice acts as a “blanket” over the otherwise open arctic waters during all months between late August and early April. If Arctic sea ice recedes from today's levels those seven months of the year, MORE energy is lost every minute by increased evaporation heat losses, increased convection heat losses, increased conduction heat losses, and increased radiation heat losses from the now-open ocean than can be gained by the fleeting moments of low-angle solar exposure each day at noon.
True, between May and early August, the exposed Arctic waters due absorb more solar energy than they lose by evaporation, radiation, and convection. But, only during those months.
The rest of the time?
Loss of Arctic sea ice from today's levels seven months of the year means increased loss of heat energy to space.
Gains in Antarctic sea ice in ANY month of the year means increased reflection of solar energy, and increased loss of heat energy into space!
It is the Antarctic sea ice extents that matters. You are wrong. The propaganda you are quoting is wrong.