I needed to find a way to modify which buttons are shown, but only in the WPBakery Page Builder TinyMCE instance, and only in the editor that corresponds to my shortcode, so as not to interfere with any other plugins.

I decided to share the solution on the WordPress StackExchange site because it’s somewhat non-obvious. I’m also posting the solution here for SEO purposes :-p

There are two technical issues:

1. As discussed above, the tiny_mce_before_init filter does not affect the TinyMCE editor that WPBakery Page Builder instantiates for parameters with param_name == 'content' and type == 'content_html'. The Page Builder frontend gets the TinyMCE HTML markup in a separate AJAX request. The editor’s instantiation does not benefit from the tinyMCEPreInit inline JavaScript array that the filter affects. The solution is to introduce a TinyMCE plugin that modifies the editor’s settings on the client side.
2. Any TinyMCE plugin must be loaded after the editor itself (see here). Even though according to the wp_enqueue_script() documentation you would expect to be able to enqueue your plugin by setting a dependency to the built-in tiny_mce script, this does not work because TinyMCE is loaded differently. See here for a discussion of the problem and a solution.

The solution: Modify the WPBakery Page Builder TinyMCE with a JavaScript plugin

We’ll first bind to tiny_mce_before_init, but not to modify the buttons. We’ll only use it to add a custom TinyMCE plugin which all editors will run. Being the creative type, I’ll call it myplugin:

function filter_tiny_mce_before_init( $mceInit ) {
    $mceInit['plugins'] .= ',myplugin';
    return $mceInit;
}

add_filter( 'tiny_mce_before_init', 'filter_tiny_mce_before_init' );

Our plugin will first check to see if the current TinyMCE editor is a WPBakery Page Builder editor. Then it will use jQuery to determine if its corresponding shortcode starts with “myplugin”:

'use strict';
tinymce.PluginManager.add( 'myplugin',
    function(editor, url) {

        // skip editors that don't belong to the Page Builder
        if ( editor.id != 'wpb_tinymce_content' )
            return;

        // skip editors that don't belong to my shortcode
        if ( !jQuery( '#wpb_tinymce_content' ).parents(
            '[data-vc-shortcode^="myplugin"]' ).length )
            return;

        // these are the only buttons we'll show
        editor.settings.toolbar1 = 'bold,italic,underline,strikethrough,link,unlink,wp_fullscreen';
        editor.settings.toolbar2 = 'pastetext,removeformat,charmap';
    } );

function action_after_wp_tiny_mce() {
    printf( 
        '<script type="text/javascript" src="%s"></script>', 
        plugins_url( 'assets/scripts/myplugin-tinymce.js', __FILE__ ) );
}

add_action( 'after_wp_tiny_mce', 'action_after_wp_tiny_mce' );