URL rewrite parameter lost (add_rewrite_rule)

The URL is then example.com/myslug (where myslug is the
permalink from the page). There is no model parameter however.

That happens because you used the wrong parameter for the Page ID:

The p parameter corresponds to a fixed page ID I have created.

So actually, for the page post type, i.e. Pages, you should use page_id and not p. See the documentation for more details.

So you just need to replace the index.php?p= with index.php?page_id= and your rewrite rule will work correctly, but remember to flush the rewrite rules manually via the Permalink Settings admin page. (Simply visit the page and WordPress will automatically flush the rules without you having to click the Save Changes button)