Ways to show multiple, separate galleries per post?

If possibile, use NextGen Gallery plugin, to manage the gallery, and with the help of custom fields, manage it in the post

You can create two custom fields, like:

1. first_gallery
2. second_gallery

and fill it with the nextgen gallery ID. You can do a custom metabox with a select box, if you want.

The in the frontend code, use

   $first = get_post_meta($post->ID, 'first_gallery',true);
   $second = get_post_meta($post->ID, 'second_gallery',true);
   ...
   echo do_shortcode('[nggallery id='.$first.']');
   echo do_shortcode('[nggallery id='.$second.']');
   ...

Hope this it helps.

Bonus: there are many nextgen gallery plugins that let you change how the gallery is rendered to the user.