15 miles seems close to me at 1 knots of current we would see silt come ashore in 15 hours in easterly wind. We know currents can be in easterly direction from the Rose Noel drifted onto Great Barier over a 100 days drifting back against prevailing wind. 60 miles would be three days and much safer.
To clarify this a little, Wind does not create, nor does it alter the course of the current that flows up the East Coast. Wind against a current causes the Sea state to increase. The sediment will not "blow" onto the Islands Coast. A floating object can and will be influenced by the Wind, with the influence being proportional to the amount of its surface is clear of water and thus influenced by the Wind.
The sediment should run with the current and in many respect, be little different than a River in flood, of which that River is capable of moving a heck of a lot more silt than any barge can.