The problem I see here is that the energy flows and pathways required are of such a magnitude and are so complex that the simplistic modelling being used basically ignores it.
For every kilotonne of ice being calved, it will require, at a minimum, the energy stored in 4 kilotonnes of sea water at 20 degrees Celcius. The resulting temperature of that sea water would be reduced to just above freezing point of water. If you, say, set the limit at a 1 degree Celsius drop, then we are looking extracting the energy of about 84 - 85 kilotonnes of sea water. You still need to take into account the energy conduction through water and also from water to the ice.
At this end of the globe, we see stories often enough of the end of small icebergs that have calved off the Antarctic ice mass. Many of these have been tracked from the initial calve to their final demise and it takes many years for even small ones to finally disappear.
To get any serious ice melt, you have to have serious amounts of energy flowing into that ice.
One question to ask is how the calving is occurring? There can be a variety of ways this can happen and they are not all caused by temperature increases. This, in itself, is a very interesting subject and there are some quite complex processes involved.
The world around us is extremely complex and we have very little understanding of how things work, irrespective of what is portrayed in popular media.
Historical records do indicate that the Arctic Polar ice mass has been of varying sizes. Some of these have essentially indicated that the ice mass was very small at some points in history and at other times very large. Some of these records and reports go back many hundreds of years.