Apply CsvHelper custom converter to all string properties of a set of classes

I'm using Josh Close's excellent CsvHelper library to read csv files and load them into a database using entity framework. This all works well except for one thing; CsvReader stores an empty string in the csv file as an empty string in the database and I would like this to be a NULL value instead. So what I've done is create a custom converter that takes care of this:

public class NullStringConverter : StringConverter { public override object ConvertFromString(TypeConverterOptions options, string text) { if (string.IsNullOrEmpty(text)) return null; else return base.ConvertFromString(options, text); } }

I can apply this to a string property by using a either fluent map syntax or via an attribute and it will now insert a NULL instead of an empty string.

Since I have quite a few classes containing a number of string attributes I would like to avoid having to create Map statements for each and everyone of them. I created a generic Map class that enumerates all properties and applies the custom converter to all string properties. Here's what I have sofar

public class DefaultStringMap<TEntity> : CsvClassMap<TEntity> where TEntity : AbstractAmtSourceEntity
{
    public DefaultStringMap()
    {
        typeof(TEntity).GetProperties()
            .Where(p => p.PropertyType == typeof(string))
            .ToList()
            .ForEach(p => Map(m => p.Name).TypeConverter<NullStringConverter>());
    }
}

Here AbstractAmtSourceEntity is my base class for all my entity classes. This doesn't work however, the mapping is not applied, so obviously I'm missing something. Can anyone tell me what's missing here?