Fixing the content

My posts are all like this:

[gallery 1]
<img>
blurb 1
<!--more-->
blurb 2
[gallery 2]
blurb 3
etc

In my theme the loop calls
the_content();
Somehow it doesn’t respect the more tag in the posts. It shows blurb 1-3 all to the end.

If I change it to the excerpt it seems to cut at the right place, but then I need more code to get the read more tag back.

I saw in https://codex.wordpress.org/Template_Tags/the_content
under Overriding Archive/Single Page Behavior
I can use

<?php
global $more;    // Declare global $more (before the loop).
$more = 0;       // Set (inside the loop) to display content above the more tag.
the_content("More...");
?>

This now shows

[gallery 1]
<img>
blurb 1
<!--more-->

But I want to strip all img and gallery from the excerpt because the featured thumb is already there.

What should I do?