$_POST array empty even though AJAX POST request came back as 200/ok?

Question

I've looked through several question/answer combinations relating to my issue, but the suggestions I've tried haven't worked.

This is my my AJAX request:

$('#submitRequest').on('click', function() {
    // package everything to get it ready for transfer
    var textSamples = JSON.stringify(packTextStyles());
    var swatches = JSON.stringify(packSwatches());
    var clientInfo = JSON.stringify(packClientInfo());

    $.ajax ({
        type: 'post',
        url: 'classes/requestHandler.php',
        //headers: {'Content-Type': 'application/json'},
        data: {
            typeSamples: textSamples,
            swatchSamples: swatches,
            userInfo: clientInfo
        },
        success: function(data) {
            if (data === 'added') {
                alert('ok');
            }
            else {
                alert(data);
                return false;
            }
        }
    });
    return false;
});

The three vars textSamples, swatches, and clientInfo are all arrays. The textSamples array contains eight objects with each having five properties, so it's a good chunk of data being sent over. My problem is that var_dump($_POST) returns an empty array and any attempt at trying json_decode($_POST['typeSamples']) gives me an error of undefined index on PHP side.

Here is the screenshot of the headers on the network tab in Chrome dev tools:

So $_POST is getting something, but I have no idea where it's going. Some questions:

1. Do I need to put headers: {'Content-Type': 'application/x-www-form-urlencoded'} or headers: {'Content-Type': 'application/json'} in the AJAX, since I used JSON.stringify()?

2. Because I used AJAX I didn't put method="post" action="something.php" in the form tag, and the input tags don't have the name attributes. Submit button doesn't have type="submit". Does that matter?

EDIT: If it matters, I'm using jQuery 1.11.1 and PHP 5.4.12

EDIT2: half-finished PHP:

<?php


$reqGetter = new RequestReceiver;
$reqGetter->checkInput();


class RequestReceiver{
    // public function __construct() {
    //  $textSamples = json_decode($_POST['typeSamples']);
    // }
    public function checkInput() {

        if (!empty($_POST)) {
            echo('added');
            $typeSamples = json_decode($_POST['typeSamples'], true);
            print_r($typeSamples);
        } else {
            echo('failed');
        }
    }
}