Works, but always adds more button, even if there's only one paragraph.

auto-read-more.php

<?php
function the_content_readmore($more_link_text = null, $stripteaser = 0) {
	$content = get_the_content($more_link_text, $stripteaser);
	$content = apply_filters('the_content', $content);
	$content = explode("</p>", $content);
	foreach ($content as $key => $value){
		if 	($value != null || $value != ''){
			if (  !stripos( $content[$key], '<iframe' )  === false ){
				echo $content[$key];
				for($i = $key+1; $i < count($content); $i++  ){
					echo $content[$i];
					if 	($content[$i] != null || $content[$i] != '') break;
				}
			}
			else{
				for($i = $key; $i < count($content); $i++  ){
					echo $content[$i];
					if 	($content[$i] != null || $content[$i] != '') break;
				}
			}	
			break;						
		}
		else echo $value;
	}
	echo '<a href="javascript:void(0);" class="button button-more">Read More <i class="fa fa-lg fa-chevron-circle-down"></i></a>';
}

Total rewrite but this should do what you want: https://gist.github.com/kerihenare/9557715