Custom media upload content for inserting custom post shortcode

I’m working on a plugin that creates custom post type “portfolio” along with shortcode to insert in any page or post.

The shortcode is: [portfolio option1=“1” option2=“0” option3=“1” ]

And it works just fine, it shows all custom posts via custom WP_query. But I want to go further.

Create a custom button next to upload media for generating a portfolio shortcode output, where user can select which post to include and define all options.
So the output would be: [portfolio option1=“1” option2=“0” option3=“1” ids=“12,311,432,443,” ]

This is the code for a button I found in wp’s media.php:

add_action( 'media_buttons', array( $this, 'media_buttons' ) );

public function media_buttons($editor_id = 'content') {
    $post = get_post();
    if ( ! $post && ! empty( $GLOBALS['post_ID'] ) )
        $post = $GLOBALS['post_ID'];

    wp_enqueue_media( array(
        'post' => $post
        ) );
    $img = '<span class="wp-media-buttons-icon"></span> ';

    echo '<a href="#" id="insert-media-button" class="button insert-media add_media" data-editor="' . esc_attr( $editor_id ) . '" title="' . esc_attr__( 'Add Portfolio' ) . '">' . $img . __( 'Add Portfolio' ) . '</a>';
}

And it does what does. But, now, what it the best way to modify the content of created window? Here’s a picture of how I see it, it’s better that any description:

How potentially complicated and tricky this would be to accomplish?
I do not know what direction should I look to, is that even possible? Please advise any suggestions where should I start digging for solution.

P.S.: Or maybe I’m wrong in the first place and should consider using ThickBox? But I want to the keep native look of the media upload popup.

Cheers!

EDIT:

Well, maybe a much better solution would be to use native gallery shortcode pattern. It not difficult to add a new menu item in the media upload window, as it explained for example here.

So the final vision is something like this:

It must be done with Backbone.js I believe? But the main question, can it manipulate custom posts instead of images?