How to execute Google App script from external script

I am attempting to build a web app that will create a Google Doc from a template and populate it with user provided data. Using Google's quickstart example in the documentation, I can successfully authorize and access the Google Drive file system. Now I need to programmatically open a template Google Doc (or even create one from scratch) and add the data.

This is rather easily done using App Script's Document Service (the DocumentAppclass). So I can do something like:

function createDoc(contentArray) {
  var doc = DocumentApp.create('Sample Document');
  var body = doc.getBody();
  var rowsData = contentArray; // data submitted with HTML form passed as arg
  body.insertParagraph(0, doc.getName())
      .setHeading(DocumentApp.ParagraphHeading.HEADING1);
  table = body.appendTable(rowsData);
  table.getRow(0).editAsText().setBold(true);
}

in a standalone App Script and successfully create the new Google Doc on Google Drive. I can't figure out how to execute this App Script from my external web app. Is there a way to do this or do I need to find a different way to create Google Docs (and add content) using just the Drive API?

EDIT:

here is the GET request from my web app:

var gurl = "https://script.google.com/macros/s/AKfycbwMHKzfZr1X06zP2iEB4E8Vh-U1vGahaLjXZA1tk49tBNf0xk4/exec";
$.get(
    gurl,
    { name: "john", time: "2pm",},
    function(data) {
      console.log(data);
    },
    "jsonp"
)

and here is my doGet():

function doGet(e) {

  var result = "";
  var name = e.parameter.name;

  Logger.log(name);

  try {
    result = "Hello " + name;
  } catch (f) {
    result = "Error: " + f.toString();
  }

  result = JSON.stringify({
    "result": result
  });  

  var doc = DocumentApp.create('ballz3');
  var body = doc.getBody();
  var rowsData = [['Plants', 'Animals'], ['Ficus', 'Goat'], ['Basil', 'Cat'], ['Moss', 'Frog']];
  body.insertParagraph(0, doc.getName())
      .setHeading(DocumentApp.ParagraphHeading.HEADING1);
  table = body.appendTable(rowsData);
  table.getRow(0).editAsText().setBold(true);
  Logger.log('DOc Name: ' + doc.getName());

  return ContentService
  .createTextOutput(e.parameter.callback + "(" + result + ")")
  .setMimeType(ContentService.MimeType.JAVASCRIPT);   

}