As you pointed out yourself [1], the iceberg is causing problems already by melting into the local ecosystem. A radioactive iceberg melting into the local ecosystem seems likely to be worse.
Nuclear bombs can be very clean these days. They've come a long way since the 1950's.
Do you really think nukes will only affect the ice? No effect on the ocean environment and sea floor beneath the berg? Surely to maximise the disruption of the ice sheet you'd need to explode the nukes underneath it. Otherwise you'll need to use more nukes, and even exploded on the surface they're still going to blast and cook a fair swathe of ocean and sea floor.