I noticed a possible issue with the code generation, which may cause the issues with excessive heap allocation that were reported:

  var code = 'return {\n';
  columns.forEach(function(column) {
    code += '"' + column.name + '":' + 'parser.readColumnValue(),\n';
  });
  code += '};\n';
  var parseRow = new Function('columns', 'parser', code);

Instead of performing so many appends to a single string, I would try using map() and then join() the resulting strings:

  var code = ['return {\n',
    columns.map(function(column) {
      return '"' + column.name + '":' + 'parser.readColumnValue(),\n';
    }).join(''),
    '};\n'].join('');

  var parseRow = new Function('columns', 'parser', code);

Of course, this depends on how often the parseRow function is created...