You can try to get as much of the string to be in contact with the ice as possible. Might be start off a water that's a bit cooler. Trial and error a few times?
If that still doesn't work, I think after you have left the string in contact with the ice for a minute or two, you can dip more string into the water to wet it and place the wet string on the string already on the ice. This will help to dilute the salt water on the top of the ice more?