If you measure, the chest will depress the ship a fraction into the water.As best I remember the weight of glacial ice on a tectonic plate is as minuscule as the weight of an ice chest on cruise ship.
The tectonic plates are between 20 and 200 kilometres thick, an ice layer of 3 kilometres thickness will add anything from a huge % weight increase to one that is quite small.
As the tectonic plate under Scandinavia is around 60 km ( 10 to 100 km) , a 3 km layer is a significant weight increase!
https://www.ngu.no/en/topic/why-are-there-mountains-norway
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