You might try using the handles on a pair of channel lock pliers through the top of the basket to hold the basket from turning when you turn the nut. It would take a helper to hold the pliers, probably with a screwdriver or other bar. This will ruin the basket, but if you're replacing it anyway, no loss. Yes, you can remove the sink now, but you'll still be faced with the same problem. At least now the sink is being held solidly while you work on it.