and in Shortcodes

Content in my shortcodes are getting wrapped in <p> or
by wpautop(). I’ve read in forums that putting shortcodes on their only lines should prevent this – but not so. I’ve tried it in the Visual Editor, the HTML editor, putting items on their own lines in various ways.

I do not want to disable wpautop() as it comes in handy everywhere else for the end-user.

In my shortcode I want the author to be able to use headings and other rich text. This may be part of the issue (but shouldn’t be as far as I have read).

I’ve found complicated solutions like this: http://betterwp.net/17-protect-shortcodes-from-wpautop-and-the-likes/

And simpler solutions like adding the following to functions.php:

remove_filter( 'the_content', 'wpautop' );
add_filter( 'the_content', 'wpautop' , 99);
add_filter( 'the_content', 'shortcode_unautop',100 );

Does anyone have a suggestion for the best way to hand this situation?
(Note: due to various reasons, I do not want the client writing the html that the shortcode creates).

My shortcode example:

[col1]
<h1>Heading</h1>
Lorem ispum
[/col1]

function col1_shortcode($atts = null, $content = null){
   $col = '<div class="col1">' . $content . '</div>';
   return $col;
}

unwantedly returns empty <p>

<div class="col1">
<p></p>
<h1>Heading</h1>
<p>Lorem ispum</p>
<p></p>
</div>

Thanks for the advise!
Brad