In order to deal with the floating plastic mines, an innovative approach is in order. How about using a helicopter, such as the MH-53E
to tow an oil skimmer. The floating mines would be separated from the water in much the same way as an oil slick. Towing with the helicopter would allow the skimmer to be unmanned. The process would resemble the operation of the ball retriever at a driving range.
Update 2:31 AM - Option 2 is to string some logs together to create floating booms. These would be arranged in a vee to create a de facto weir. Then use the downwash of multiple helicopters to blow the mines into the weir. In effect, its round up time at the OK Corral!