I'm dumb when it comes to science. But if the worst case scenario happens, couldn't we build facilities to 'dispose' of the melted ice in any way, instead of letting the sea level rise?
That said, any time you consider any geoengineering idea, you have to make the argument that the $1 trillion or whatever you'd spend on solar radiation management or ice shelf preservation or whatever, would not be money better spent on just transitioning away from fossil fuel use.
It would require a lot of energy, but all remedies to climate change require that.
Where does all the energy go if it does not go into raising the temperature?
The Gulf Stream does exactly what is suggestion, moving massive amounts of warm water north and it's effect on winter temperatures in Western Europe is massive.
Surface area of Earth = 510 million km^2 = 5.10e14 m^2.
~70% is water, so 3.57e14 m^2.
Multiply that by 3mm (3e-3 m) = 1.07e12 m^3.
1.07 trillion tonnes of water. Per year.
Or 33,907 tonnes per second!
Actually the Hoover dam streams 2000 tons per second [1]. So we may not be far off!
Basically build 15 Hoover dams worth of nuclear plants in Antarctica and their plumbing.
Expensive? Yes. But also quite doable especially compared to cost of losing coastal cities.
1. https://www.nps.gov/nr/travel/ReclamationDamsIrrigationProje...