You can filter the_content_more_link
hook and remove #more-POST_ID
from the link:
function wpse_51806_strip_more_link( $more_link ) {
global $id;
return str_replace( "#more-$id", '', $more_link );
}
add_filter( 'the_content_more_link', 'wpse_51806_strip_more_link' );
It has even been made into a plugin, if you’re more comfortable with plugins then code snippets.