Add attributes to ACF inner blocks

ACF has introduced inner block support which I'd like to use.

Via my block template, I have the following:

<?php
$allowed_blocks = array( 'core/heading', 'core/paragraph' );
echo '<InnerBlocks allowedBlocks="' . esc_attr( wp_json_encode( $allowed_blocks ) ) . '" />';

This limits the block editor to headings and paragraphs only.

Is it possible to add a class attribute to each heading and paragraph? For example, <p class="block__paragraph">.

I'm aware I can achieve this with str_replace but I wondered if there's a more efficient way to hook into InnerBlocks?

I'm also aware you can use templates, like so:

<?php
$template = array(
    // Heading
    array( 'core/heading', array(
        'level' => 2,
        'placeholder' => 'Add a Title',
        'className' => 'block__heading',
    ) ),
    // Paragrph
    array( 'core/paragraph', array(
        'className'    => 'block__paragraph',
        'placeholder'  => 'Write your text.',
    ) ),
);
echo '<InnerBlocks template="' . esc_attr( wp_json_encode( $template ) ) . '" templateLock="false" />';

However, this limits the editor to a set number of blocks.