Pages & Search widgets on each of multiple widgetized sidebars?

I have registered 3 sidebars (plus one more footer sidebar):

if ( function_exists('register_sidebars') )
	register_sidebars(3, array(
		'name' => 'Sidebar %d',
		'before_widget' => '<div id="%1$s" class="widget_style"><div class="side_left">
                                    	<div class="side_right">
                                        	<div class="side_top">
                                            	<div class="side_bot">
                                                	<div class="left_top">
                                                    	<div class="right_top">
                                                        	<div class="left_bot">
                                                            	<div class="right_bot">',
		'after_widget' => '</div>
                            	</div>', 

		'before_title' => '<p class="widget_title">',
		'after_title' => '
</div>
                                                            </div>
                                                        </div>
                                                    </div>
                                                </div>
                                            </div>
                                        </div>
                                    </div>
                                    <div class="inside_widget_2">',
	));

if ( function_exists('register_sidebar') )
	register_sidebar(array(
		'name' => 'Footer Widgets',
		'before_widget' => '<div id="%1$s" class="widget_style"><div class="side_left">
                                    	<div class="side_right">
                                        	<div class="side_top">
                                            	<div class="side_bot">
                                                	<div class="left_top">
                                                    	<div class="right_top">
                                                        	<div class="left_bot">
                                                            	<div class="right_bot">',
		'after_widget' => '</div>
                            	</div>', 

		'before_title' => '<p class="widget_title">',
		'after_title' => '
</div>
                                                            </div>
                                                        </div>
                                                    </div>
                                                </div>
                                            </div>
                                        </div>
                                    </div>
                                    <div class="inside_widget_2">',
	));

(sorry for all the <div> glop in there, but it works)

and then I try to call just one sidebar in the sidebar.php file using:

<?php if ( !function_exists('dynamic_sidebar')
|| !pick_sidebar() ) : endif; ?>

The pick_sidebar() function I created in the functions.php file:

function pick_sidebar() {
	if (is_home()) {dynamic_sidebar('Sidebar 1'); }
	elseif (is_page()) {dynamic_sidebar('Sidebar 2');}
	else {dynamic_sidebar('Sidebar 3');}
	}

This works fine, and I can get different widgets and everything at the right places (haven’t tested extensively, though).

My problems is that when I go to add widgets, I can only add one “pages” widget TOTAL for ALL of the sidebars, not to each sidebar. I want to be able to add a pages widget to each of the sidebars. What am I doing wrong?
p.s. I’m new to PHP