Set Background Image from Custom Meta in WordPress

I’m trying to get the home page of a WordPress theme I am building to change the background image on refresh based on 3 potential background images.

Each image is considered part of a larger “case study” that has a title, link, text, etc.
The case study fields are created through custom meta boxes on the home page. (I am using this to simplify the meta box creation process: https://github.com/jaredatch/Custom-Metaboxes-and-Fields-for-WordPress).

Long story short, the client wants 3 case studies on the home page to have corresponding background images. This is why I didn’t use the featured image functionality, as each background goes with specific meta data.

The problem is, I can’t figure out how to get the meta ID of the chosen background image and use that to set the background CSS.

Here is what I have so far:

/**
 * Home Page Case Randomizer
 */

$GLOBALS['_home_case_number'] = rand(1, 3);


function home_case_number() {

   if ( is_front_page() ) :  // checks whether this is the home page

    // get the meta image
$attachment_image = get_post_meta( get_the_ID(), '_home_case_background_' . $_home_case_number, true );

This is where I get confused. The above returns the appropriate image.jpg file. How do I massage this to work with the below code?

The below code is adapted from http://s2webpress.com/responsive-featured-image-function-in-wordpress-themes/, and I’d like to use it to make sure I’m serving images responsively.

// store the image sizes in an array
$img_sizes = array( 'thumbnail', 'medium', 'large', 'full' );

// grab the URL for each image size and store in a variable
foreach ( $img_sizes as $img_size ) {
    ${ 'img_src_' . $img_size } = wp_get_attachment_image_src( $attachment_image, $img_size );
}




echo '<style type="text/css"> 

    .featured-image {

        width: 100%;        
        min-height:350px; 
        background-image: url(' . esc_url( $img_src_medium[0] ) . ');
    }


    @media screen and ( min-width: 400px ) {
        .featured-image {
            background-image: url(' . esc_url( $img_src_large[0] ) . ');
        }
    }

    @media screen and ( min-width: 1000px ) {
        .featured-image {
            background-image: url(' . esc_url( $img_src_full[0] ) . ');
        }               
    }


</style>';

endif;
 };


add_action( 'wp_head', 'home_case_number' );

So do I go about this by getting the meta ID of the background image? Or the attachment ID? I don’t know how to do either at this point.

Any help is much appreciated!