Pumping >0C water onto the remaining ice will accelerate the melting
No, not in winter.
The problem in winter is that ice (and snow on top of it) is a good insulator that, once the ice reaches around 1-2m thick causes it to continue to thicken very slowly.
It's one of the reasons why the sea ice minimum is falling faster than the maximum - the arctic winter is cold enough to (almost) completely refreeze every year but that resultant ice isn't thick enough to survive a summer season. That's why there's so much interest in tracking the multi-year ice. That's the thick stuff.
Unfortunately, measuring volume is much harder to do so ice extent and ice area tend to take centre stage even if they're not the best metric for the state of the ice in the arctic.
Pumping water to the top of the ice would allow the ice to thicken much more than it currently can in a single winter.