Changing a specific value inside a complex repeater/flexible content field (ACF)

Answering my own question again. 😛
I finally found this Gist that lets me get and set array variables via dot notation:
https://gist.github.com/elfet/4713488

So I included the DotNotation class and now my code looks like this (skipping all sorts of error checking here) :

$fieldmap_string = 'key1.key2.key3.etc';
$current_page_content = get_field('page_content', $source_post_id);
$parsed_current_content = new DotNotation($current_page_content);
$image_field_value = $parsed_current_content->get($fieldmap_string);

$target_page_content = get_field('page_content', $target_post_id);
$parsed_target_content = new DotNotation($target_page_content);
$parsed_target_content->set($fieldmap_string, $image_field_value);
$new_page_content = $parsed_target_content->getValues();
update_field('page_content', $new_page_content, $target_post_id);

Works like a charm.